Gerard manley hopkins terrible Essay Example For Students

Gerard manley hopkins terrible Essay Gerard Manley Hopkins terrible SonnetsIn the mid 1800s a very spiritual poet was born. Gerard Manley Hopkins was born July 28, 1844 to Manley and Catherine (Smith) Hopkins, the first of their nine children (Drabble 473). His parents were High Church Anglicans, and his father had just published a volume of poetry the year before (Drabble 473). He was ordained as a Jesuit priest who wrote beautiful poetry full of thoughts of nature and harmony. Hopkins poetry was, for the most part, published after his death in 1889. Five years before Hopkins death he wrote six terrible sonnets revealing his inner torment and separation from God (Davie 86). These poems were written while Hopkins worked as a professor at University College, Dublin (Drabble 474). Hopkins sonnets No Worst, there is none and I wake and feel the fell of Dark, Not Day show his mental anguish caused by spiritual agony. His job as a professor at University College required the grading of 500 examination papers, each one sever al pages of uninspired student translations, five to six times a year (Benzel 370). His job demanded long hours which took away time for his admiration of nature and his time for prayer. The six terrible sonnets have a strong contradiction to his earlier works. His early works were filled with beautiful scenes in nature and praise of God. His realization that he was not dedicating enough time to God allowed him to see how many other people lose sight of God. This and other experiences during the time while he wrote his terrible sonnets allow us to assume that the poems are his own religious confessions. More important, however, was his sense that his prayers no longer reached God (Benzel 371). Hopkins life-long best friend Robert Bridges received several letters from Hopkins while he wrote the terrible sonnets. Hopkins wrote to Bridges that the sonnets came to him like inspirations unbidden and against my will (Leavis 5296). Hopkins saw in his poems the fragmentation of his capacity to represent his Christian vision adequately. Hopkins considered this poetry the wrong kind of poetry because the sonnets did not manifest that penetrating delineation, that inscaping of Christ in nature which had formerly been his joy (Leavis 5297). Though Hopkins felt these poems were wrong and unwanted he also name them inspirations which meant that he recognized their poetic merit and their spiritual worth. His recognition of his losing touch with God in nature is a way of asking God for forgiveness (Leavis 5297). The sonnet No worst, there is none reveals Hopkins lowest pit of desolation and inner torment caused from his distance with God. Mariani notes the sonnet only contains only a few images of nature and is all darkness. The sonnet can be divided into two parts. The first ten lines of the poem present his despair. Lines one and two No worst there is none. Pitched past pitch of grief / More pangs will, schooled at forepangs, wilder wring (ll.1-2), reveal he has touched bottom: Hopkins, like a violin string, is strung tighter to play at the higher, more piercing and metallic tone of grief (Mariani 59). Line one suggest an inexpressible degree of pain (Benzel 382). Line two turns the grief into something horrifyingly active.Lines three and four Comforter, where, where is your comforting? / Mary, mother of us, where is your relief? (ll. 3-4), almost admonishes the Blessed Virgin and the comforter, who is Christ as well as the Holy Spirit, for not coming to his aid. Line six woe, world sorrow ; on a age-old anvil wince and sing, is Hopkins terrifying realization that man, rebellious creature, is unworthy of Gods concern (Mariani 60). In line six The anvil wincing and singing and furys shrieking force the sense of physical pain on us again and turn the screw tighter (Benzel 382). Line nine and ten O the mind, mind has mountains; cliffs of fall / Frightful, sheer, no-man-fathomed. Hold them cheap (ll. 9-10), refer to mans original fall and severance from God. The last few lines uncover Hopkins relief from his despair.These lines portray Hopkins anguish by his admitting to looking forward to

The Effects of Solons Reforms on Athens Essay Example

The Effects of Solons Reforms on Athens Paper Athens, pre-574 BC, was riddled with problems, and the nobles of Athens soon realised that the revolt, resulting in a tyranny that had happened in so many surrounding cities, was a serious possibility. Their solution was to shift law making power to Solon. Solon soon revolutionised Athens by an attempt to solve the political, economic and social problems of Athens. Before Solons reforms, the political situation in Athens was not desirable. Split into 3 levels; the magistrates, nobles and held the majority of power; the Council of Areopagus, nobles who controlled the law and the state; and the Assembly, the middle classes of Athens who held little power, the government was used by nobles to exploit the poor. Solon endeavoured for Eunomia; or the reign of good order, where all classes where represented in government. Under Solons leadership, the Codes of Law, regarding family matters, were revised and brought benefits to all social classes. He established a Timocracy; a government in which political rights of citizens were determined by wealth, not by birth. He then split the government into 5 levels; the archons, the Council of Areopagus, The Council of 400, the Assembly and the Heliaea. By spreading the power evenly over the 5 levels and allowing men of non noble birth and lower income into government, Solon broke the monopoly the nobles had held over the government and set the foundation for a democracy. We will write a custom essay sample on The Effects of Solons Reforms on Athens specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on The Effects of Solons Reforms on Athens specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on The Effects of Solons Reforms on Athens specifically for you FOR ONLY $16.38 $13.9/page Hire Writer The economic situation in Athens was also extreme. Widespread debt, the rising of the Hektemoroi, and Athens war against Megara, all resulted in a struggling Athens. Solon immediately passed the Seisachtheia, or the shaking off of burdens. This meant that all outstanding debt was cancelled, and all those who had become slaves due to their debt were freed. It also involved the return of those who had been sold overseas, and the removal of the Hektemoroi. As a result, Athens became a city filled with peasants who had no money or land. The wealthy of Athens lost control over large areas of land on which the Hektemoroi had worked, and they also lost the interest on their loans. Solon also placed temporary bans on exports or agricultural products to prevent famine. This prevented speculation in essential products and lowered the prices on basic necessities. He encouraged many of the landless to return to learning a craft, and made it obligatory for the father to teach his son a trade. These reforms took steps to making Athens a free citizen nation, but it only alleviated distress instead of eliminating the problems. Pre 574, Athens was split up into 4 social classes; the Eupatridae, nobles that held almost all political power; the Georgoi and Demiourgoi, farmers and craftsmen who held average rights; and the Thetes, who held no political rights or land. These classes also split into clans, the constant bickering between clans often disrupting Athens. Solons reforms meant that all 4 classes held political power, and it was more difficult for the Eupatridae to exploit the other classes. Fighting between clans also decreased, and Athens became much more stable. In conclusion, we can clearly see that Solon attempted to address all major issues prevalent in Athens at the time, from debt to social classes. His reforms aided the situation, but whether his reforms were practical for long term application is arguable.

Sequences on ACT Math Strategy Guide and Review

Sequences on ACT Math Strategy Guide and Review SAT / ACT Prep Online Guides and Tips Sequences are patterns of numbers that follow a particular set of rules. Whether new term in the sequence is found by an arithmetic constant or found by a ratio, each new number is found by a certain rule- the same rule- each time. There are several different ways to find the answers to the typical sequence questions- †What is the first term of the sequence?†, â€Å"What is the last term?†, â€Å"What is the sum of all the terms?†- and each has its benefits and drawbacks. We will go through each method, and the pros and cons of each, to help you find the right balance between memorization, longhand work, and time strategies. This will be your complete guide to ACT sequence problems- the various types of sequences there are, the typical sequence questions you’ll see on the ACT, and the best ways to solve these types of problems for your particular ACT test taking strategies. Before We Begin Take note that sequence problems are rare on the ACT, never appearing more than once per test. In fact, sequence questions do not even appear on every ACT, but instead show up approximately once every second or third test. What does this mean for you? Because you may not see a sequence at all when you go to take your test, make sure you prioritize your ACT math study time accordingly and save this guide for later studying. Only once you feel you have a solid handle on the more common types of math topics on the test- triangles (comng soon!), integers, ratios, angles, and slopes- should you turn your attention to the less common ACT math topics like sequences. Now let's talk definitions. What Are Sequences? For the purposes of the ACT, you will deal with two different types of sequences- arithmetic and geometric. An arithmetic sequence is a sequence in which each term is found by adding or subtracting the same value. The difference between each term- found by subtracting any two pairs of neighboring terms- is called $d$, the common difference. -5, -1, 3, 7, 11, 15†¦ is an arithmetic sequence with a common difference of 4. We can find the $d$ by subtracting any two pairs of numbers in the sequence- it doesn’t matter which pair we choose, so long as the numbers are next to one another. $-1 - -5 = 4$ $3 - -1 = 4$ $7 - 3 = 4$ And so on. 12.75, 9.5, 6.25, 3, -0.25... is an arithmetic sequence in which the common difference is -3.25. We can find this $d$ by again subtracting pairs of numbers in the sequence. $9.5 - 12.75 = -3.25$ $6.25 - 9.5 = -3.25$ And so on. A geometric sequence is a sequence of numbers in which each successive term is found by multiplying or dividing by the same amount each time. The difference between each term- found by dividing any neighboring pair of terms- is called $r$, the common ratio. 212, -106, 53, -26.5, 13.25†¦ is a geometric sequence in which the common ratio is $-{1/2}$. We can find the $r$ by dividing any pair of numbers in the sequence, so long as they are next to one another. ${-106}/212 = -{1/2}$ $53/{-106} = -{1/2}$ ${-26.5}/53 = -{1/2}$ And so on. Though sequence formulas are useful, they are not strictly necessary. Let's look at why. Sequence Formulas Because sequences are so regular, there are a few formulas we can use to find various pieces of them, such as the first term, the nth term, or the sum of all our terms. Do take note that there are pros and cons for memorizing formulas. Pros- formulas are a quick way to find your answers, without having to write out the full sequence by hand or spend your limited test-taking time tallying your numbers. Cons- it can be easy to remember a formula incorrectly, which would lead you to a wrong answer. It also is an expense of brainpower to memorize formulas that you may or may not even need come test day. If you are someone who prefers to use and memorize formulas, definitely go ahead and learn these! But if are not, then you are still in luck; most (though not all) ACT sequence problems can be solved longhand. So if you have the patience- and the time to spare- then don’t worry about memorizing formulas. That all being said, let’s take a look at our formulas so that those of you who want to memorize them can do so and so that those of you who don’t can still understand how they work. Arithmetic Sequence Formulas $$a_n = a_1 + (n - 1)d$$ $$\Sum \terms = (n/2)(a_1 + a_n)$$ These are our two important arithmetic sequence formulas and we will go through how each one works and when to use them. Terms Formula $a_n = a_1 + (n - 1)d$ If you need to find any individual piece of your arithmetic sequence, you can use this formula. First, let us talk about why it works and then we can look at some problems in action. $a_1$ is the first term in our sequence. Though the sequence can go on infinitely, we will always have a starting point at our first term. $a_n$ represents any missing term we want to isolate. For instance, this could be the 4th term, the 58th, or the 202nd. Why does this formula work? Well let’s say we wanted to find the 2nd term in the sequence. We find each new term by adding our common difference, or $d$, so the second term would be: $a_2 = a_1 + d$ And we would then find the 3rd term in the sequence by adding another $d$ to our existing $a_2$. So our 3rd term would be: $a_3 = (a_1 + d) + d$ Or, in other words: $a_3 = a_1 + 2d$ And the 4th term of the sequence, found by adding another $d$ to our existing third term, would continue this pattern: $a_4 = (a_1 + 2d) + d$ Or $a_4 = a_1 + 3d$ So, as you can see, each term in the sequence is found by adding the first term to $d$, multiplied by $n - 1$. (The 3rd term is $2d$, the 4th term is $3d$, etc.) So now that we know why the formula works, let’s look at it in action. What is the difference between each term in an arithmetic sequence, if the first term of the sequence is -6 and the 12th term is 126? 3 4 6 10 12 Now, there are two ways to solve this problem- using the formula, or finding the difference and dividing by the number of terms between each number. Let’s look at both methods. Method 1: Arithmetic Sequence Formula If we use our formula for arithmetic sequences, we can find our $d$. So let us simply plug in our numbers for $a_1$ and $a_n$. $a_n = a_1 + (n - 1)d$ $126 = -6 + (12 - 1)d$ $126 = -6 + 11d$ $132 = 11d$ $d = 12$ Our final answer is E, 12. Method 2: finding difference and dividing Because the difference between each term is regular, we can find that difference by finding the difference between our terms and then dividing by the number of terms in between them. Note: be very careful when you do this! Though we are trying to find the 12th term, there are NOT 12 terms between the first term and the 12th- there are actually 11. Why? Let’s look at a smaller scale sequence of 3 terms. 4, __, 8 If you wanted to find the difference between these terms, you would again find the difference between 4 and 8 and divide by the number of terms separating them. You can see that there are 3 total terms, but 2 terms separating 4 and 8. 1st: 4 to __ 2nd: __ to 8 When given $n$ terms, there will always be $n - 1$ terms between the first number and the last. So, if we turn back to our problem, now we know that our first term is -6 and our 12th is 126. That is a difference of: $126 - -6$ $126 + 6$ $132$ And we must divide this number by the number of terms between them, which in this case is 11. $132/11$ $12$ Again, the difference between each number is E, 12. As you can see, the second method is just another way of using the formula without actually having to memorize the formula. How you solve these types of questions completely depends on how you like to work and your own personal ACT math strategies. Sum Formula $\Sum \terms = (n/2)(a_1 + a_n)$ This formula tells us the sum of the terms in an arithmetic sequence, from the first term ($a_1$) to the nth term ($a_n$). Basically, we are multiplying the number of terms, $n$, by the average of the first term and the nth term. Why does this work? Well let’s look at an arithmetic sequence in action: 4, 7, 10, 13, 16, 19 This is an arithmetic sequence with a common difference, $d$, of 3. A neat trick you can do with any arithmetic sequence is to take the sum of the pairs of terms, starting from the outsides in. Each pair will have the same exact sum. So you can see that the sum of the sequence is $23 * 3 = 69$. In other words, we are taking the sum of our first term and our nth term (in this case, 19 is our 6th term) and multiplying it by half of $n$ (in this case $6/2 = 3$). Another way to think of it is to take the average of our first and nth terms- ${4 + 19}/2 = 11.5$ and then multiply that value by the number of terms in the sequence- $11.5 * 6 = 69$. Either way, you are using the same basic formula, so it just depends on how you like to think of it. Whether you prefer $(n/2)(a_1 + a_n)$ or $n({a_1 + a_n}/2)$ is completely up to you. Now let’s look at the formula in action. Andrea is selling boxes of cookies door-to-door. On her first day, she sells 12 boxes of cookies, and she intends to sell 5 more boxes per day than on the day previous. If she meets her goal and sells boxes of cookies for a total of 10 days, how many boxes total did she sell? 314 345 415 474 505 As with almost all sequence questions on the ACT, we have the choice to use our formulas or do the problem longhand. Let’s try both ways. Method 1: formulas We know that our formula for arithmetic sequence sums is: $\Sum = (n/2)(a_1 + a_n)$ In order to plug in our necessary numbers, we must find the value of our $a_n$. Once again, we can do this via our first formula, or we can find it by hand. As we are already using formulas, let us use our first formula. $a_n = a_1 + (n - 1)d$ We are told that the first term in our sequence is 12. We also know that she sells cookies for 10 days and that, each day, she sells 5 more boxes of cookies. This means we have all our pieces to complete this formula. $a_n = 12 + (10 - 1)5$ $a_10 = 12 + (9)5$ $a_10 = 12 + 45$ $a_10 = 57$ Now that we have our value for $a_n$ (in this case $a_10$), we can complete our sum formula. $(n/2)(a_1 + a_n)$ $(10/2)(12 + 57)$ $5(69)$ $345$ Our final answer is B, 345. Method 2: longhand Alternatively, we can solve this problem by doing it longhand. It will take a little longer, but this way also carries less risk of mis-remembering a formula. The decision is, as always, completely up to you on how you choose to solve these kinds of questions. First, let us write out our sequence, beginning with 12 and adding 5 to each subsequence number, until we find our nth (10th) term. 12, 17, 22, 27, 32, 37, 42, 47, 52, 57 Now, we can either add them up all by hand- $12 + 17 + 22 + 27 + 32 + 37 + 42 + 47 + 52 + 57 = 345$ Or we can use our arithmetic sequence sum trick and divide the sequence into pairs. We can see that there are 5 pairs of 69, so $5 * 69 = 345$. Again, our final answer is B, 345. Whoo! Only one more formula to go! Geometric Sequence Formulas $$a_n = a_1( r^{n - 1})$$ (Note: there is a formula to find the sum of a geometric sequence, but you will never be asked to find this on the ACT, and so it is not included in this guide.) This formula, as with the first arithmetic sequence formula, will help you find any number of missing pieces in your sequence. Given two pieces of information about your sequence ($a_n$ $a_1$, $a_1$ $r$, or $a_n$ $r$), you can find the third. And, as always with sequences, you have the choice of whether to solve your problem longhand or with a formula. What is the first term in a geometric sequence if each number is found by multiplying the previous term by -3 and the 8th term is 4,374? -0.222 0.667 -2 6 -18 Method 1: formula If you’re one for memorizing formulas, we can simply plug in our values into our equation in place of $a_n$, $n$, and $r$ in order to solve for $a_1$. $a_n = a_1( r^{n - 1})$ $4374 = a_1(-3^{8 - 1})$ $4374 = a_1(-3^7)$ $4374 = a_1(-2187)$ $-2 = a_1$ So our first term in the sequence is -2. Our final answer is C, -2. Method 2: longhand Alternatively, as always, we can take a little longer and solve them problem by hand. First, set out our number of terms in order to keep track of them, with our 8th term, 4374, last. ___, ___, ___, ___, ___, ___, ___, 4374 Now, let’s divide each number by -3 down the sequence until we reach the beginning. ___, ___, ___, ___, ___, ___, -1458, 4374 ___, ___, ___, ___, ___, 486, -1458, 4374 And, if we keep going thusly, we will eventually get: -2, 6, -18, 54, -162, 486, -1458, 4374 Which means that we can see that our first term is -2. Again, our final answer is C, -2. As with all sequence solving methods, there are benefits and drawbacks to solving the question in each way. If you choose to use formulas, make very sure you can remember them exactly. And if you solve the questions by hand, be very careful to find the exact number of terms in the sequence. The ACT will always provide bait answers for anyone who is one or two terms off the nth term- in this problem, if you had accidentally assigned 4374 as the 7th term or the 9th term, you would have chosen answer B or D. Once you find the strategy that works best for you, the pieces will all fall into place. Typical ACT Sequences Questions Because all sequence questions on the ACT can be solved (if sometimes arduously) without the use or knowledge of sequence formulas, the test-makers will only ever ask you for a limited number of terms or the sum of a small number of terms (usually less than 12). As we saw above, you may be asked to find the 1st term in a sequence, the nth term, the difference between your terms (whether a common difference, $d$, or a common ratio, $r$), or the sum of your terms in arithmetic sequences only. You also may be asked to find an unusual twist on a sequence question that combines your knowledge of sequences. For example: What is the sum of the first 5 terms of an arithmetic sequence in which the 6th term is 14 and the 11th term is 22? 2.2 6.0 12.4 32.6 46.0 Again, let us look at both formulaic and longhand methods for how to solve a problem like this. Method 1: formulas In order to find our common difference, we can use our main arithmetic sequence formula. But this time, instead of beginning with the actual $a_1$, we are beginning with our 6th term, as this is what we are given. Essentially, we are designating our 6th term as our 1st term and our 11th term as our 6th term and then plugging these values into our formula. $a_n = a_1 + (n - 1)d$ $22 = 14 + (6 - 1)d$ $22 = 14 + 5d$ $8 = 5d$ $1.6 = d$ Now, we can find our actual 1st term by using the $d$ we just found and our 11th term value of 22. $a_n = a_1 + (n - 1)d$ $22 = a_1 + (11 - 1)1.6$ $22 = a_1 + (10)1.6$ $22 = a_1 + 16$ $6 = a_1$ The 1st term of our sequence is 6. Now, we need to find the 5th term of our sequence in order to use our arithmetic sequence sum formula to find the sum of the first 5 terms. $a_n = a_1 + (n - 1)d$ $a_5 = 6 + (5 - 1)1.6$ $a_5 = 6 + (4)1.6$ $a_5 = 6 + 6.4$ $a_5 = 12.4$ And finally, we can find the sum of our first 5 terms by using our sum formula and plugging in the values we found. $(n/2)(a_1 + a_n)$ $5/2(6 + 12.4)$ $2.5(18.4)$ $46$ Our final answer is E, 46. As you can see, this problem still took a significant amount of time using our formulas because there were so many moving pieces. Let us look at this problem were we to solve it longhand instead. Method 2: longhand First, let us find our common difference by finding the difference between our 6th term and our 11th term and dividing by how many terms are in between them, which in this case is 5. (Why 5? There is one term between the 6th and 7th terms, another between the 7th and 8th, another between the 8th and 9th, another between the 9th and 10th, and the last between the 10th and 11th terms. This makes a total of 5 terms.) This gives us: $22 - 14 = 8$ $8/5 = 1.6$ Now, let us simply find all the numbers in our sequence by working backwards and subtracting 1.6 from each term. ___, ___, ___, ___, ___, 14, ___, ___, ___, ___, 22 ___, ___, ___, ___, ___, 14, ___, ___, ___, 20.4, 22 ___, ___, ___, ___, ___, 14, ___, ___, 18.8, 20.4, 22 And so on, until all the spaces are filled. 6, 7.6, 9.2, 10.8, 12.4, 14, 15. 6, 17.2, 18.8, 20.4, 22 Now, simply add up the first 5 terms. $6 + 7.6 + 9.2 + 10.8 + 12.4$ $46$ Our final answer is E, 46. Again, you always have the choice to use formulas or longhand to solve these questions and how you prioritize your time (and/or how careful you are with your calculations) will ultimately decide which method you use. You've seen the typical ACT sequence questions, so let's talk strategies. Tips For Solving Sequence Questions Sequence questions can be somewhat tricky and arduous to slog through, so keep in mind these ACT math tips on sequences as you go through your studies: 1: Decide before test day whether or not you will use the sequence formulas Before you go through the effort of committing your formulas to memory, think about the kind of test-taker you are. If you are someone who lives and breathes formulas, then go ahead and memorize them now. Most sequence questions (though, as we saw above, not all of them) will go much faster once you have the formulas down straight. If, however, you would rather dedicate your time and brainpower to other math topics or to the method of performing sequence questions longhand, then don’t worry about your formulas! Don’t even bother to try to remember them- just decide here and now not to use them and forget about the formulas entirely. Unless you can be sure to remember them correctly, a formula will hinder more than help you when it comes time to take your ACT, so make the decision now to either memorize them or forget about them. 2: Write your values down and keep your work organized Though many calculators can perform long strings of calculations, sequence questions by definition involve many different values and terms. Small errors in your work can cause a cascade effect. One mistyped digit in your calculator can throw off your work completely, and you won’t know where the error happened if you do not keep track of your values. Always remember to write down your values and label them in order to prevent a misstep somewhere down the line. 3: Keep careful track of your timing No matter how you solve a sequence question, these types of problems will generally take you more time than other math questions on the ACT. For this reason, most all sequence questions are located in the last third of the ACT math section, which means the test-makers think of sequences as a â€Å"high difficulty† level problem. Time is your most valuable asset on the ACT, so always make sure you are using yours wisely. If you can answer two other math questions in the time it takes you to answer one sequence question, then maximize your point gain by focusing on the other two questions. Always remember that each question on the ACT math section is worth the same amount of points, so prioritize quantity and don’t let your time run out trying to solve one problem. If you feel that you can answer a sequence problem quickly, go ahead! But if you feel it will take up too much time, move on and come back to it later. Ready to put your knowledge to the test? Test Your Knowledge Now let’s test your sequence knowledge with real ACT math problems. 1. What is the first term in the arithmetic sequence if terms 6 through 9 are shown below? ...196, 210, 224, 238 7 14 98 126 140 2. What is the sum of the first 8 terms in the arithmetic sequence that begins: 7, 10.5, 14,... 143.5 154 162.5 168 176.5 3. Answers: D, B, E Answer Explanations: 1. As always, we can solve this problem with formulas or via longhand. For the sake of brevity, we will only use one method per problem here. In this case, let us solve our problem via longhand. We are told this is an arithmetic sequence, so we can find our common difference by subtracting neighboring terms. Let us take a pair and subtract to find our $d$. $238 - 224 = 14$ $d = 14$ We know our common difference is 14, and 196 is our 6th term. Let us work backwards to find our 1st term. ___, ___, ___, ___, ___, 196, 210, 224, 238 ___, ___, ___, ___, 182, 196, 210, 224, 238 ___, ___, ___, 168, 182, 196, 210, 224, 238 And so on, until we reach our first term. 126, 140, 154, 168, 182, 196, 210, 224, 238 As long as we kept our work organized, we will find the first term in our sequence. In this case, it is 126. Our final answer is D, 126. 2. Again, we have many options for solving our problem. In this case, we can use a combination of longhand and formula (in addition to the standard options of using either method alone). First, we must find our common difference between our terms by subtracting any neighboring pair. $14 - 10.5 = 3.5$ $d = 3.5$ Now that we have found our $d$, let us finish our sequence until the 8th term by continuing to add 3.5 to each successive term. 7, 10.5, 14, 17.5, 21, 24.5, 28, 31.5 And finally, we can plug in our values into our sum formula to find the sum of all our terms. $(n/2)(a_1 + a_n)$ $(8/2)(7 + 31.5)$ $(4)(38.5)$ $154$ The sum of the first 8 terms in the sequence is 154. Our final answer is B, 154. 3. Again, we can use multiple methods to solve our problem. In this case, let us use our formula for geometric sequences. First, we need to find our common ratio between terms, so let us divide any pair of neighboring terms to find our $r$. ${-27}/9 = -3$ $r = -3$ Now we can plug in our values into our formula. $a_n = a_1( r^{n - 1})$ $a_7 = 1(-3^{7 - 1})$ $a_7 = 1(-3^6)$ $a_7 = 1(-729)$ $a_7 = 729$ The 7th term of our sequence is 729. Our final answer is E, 729. You did it, you genius you! The Take Aways Sequence questions often take a little time and effort to get through, but they are usually made complicated by their number of terms and values rather than being actually difficult to solve. Just remember to keep all your work organized and decide before test-day whether you want to spend your study efforts memorizing, or if you would prefer to work out your sequence problems by hand. As long as you keep your values straight (and don’t get tricked by bait answers!), you will be able to grind through these problems without fail, using either method. What’s Next? Phew! You have officially mastered ACT sequence questions. So...now what? Well you're in luck because there are a lot more ACT math topics and guides to check out! Want to brush up on your ratios? How about your trigonometry? Coordinate geometry and slopes? No matter what ACT topic you want to master, we've got you covered. Feel like you're running out of time on ACT math? Check out our guide to help you beat the clock. Want to know the score you should aim for? Start by looking at how the scoring works and what that means for you. Looking to get a perfect score? Our guide to getting a 36 on ACT math (written by a perfect-scorer) will help you get to where you want to be! Want to improve your ACT score by 4 points? Check out our best-in-class online ACT prep program. We guarantee your money back if you don't improve your ACT score by 4 points or more. Our program is entirely online, and it customizes what you study to your strengths and weaknesses. If you liked this Math lesson, you'll love our program. Along with more detailed lessons, you'll get thousands of practice problems organized by individual skills so you learn most effectively. We'll also give you a step-by-step program to follow so you'll never be confused about what to study next. Check out our 5-day free trial:

Aftermath of World War 1 - Treaty of Versailles

Aftermath of World War 1 - Treaty of Versailles The World Comes to Paris In the wake of the November 11, 1918 armistice which ended hostilities on the Western Front, Allied leaders gathered in Paris to begin negotiations over the peace treaties that would formally conclude the war. Convening in the Salle de lHorloge at the French Foreign Ministry on January 18, 1919, the talks initially included leaders and representatives from over thirty nations. To this crowd was added a host of journalists and lobbyists from a variety of causes. While this unwieldy mass took part in the early meetings, it was President Woodrow Wilson of the United States, Prime Minister David Lloyd George of Britain, Prime Minister Georges Clemenceau of France, and Prime Minister Vittorio Orlando of Italy who came to dominate the talks. As defeated nations, Germany, Austria, and Hungary were prohibited from attending, as was Bolshevik Russia which was in the midst of a civil war. Wilsons Goals Arriving in Paris, Wilson became the first president to travel to Europe while in office. The basis for Wilsons position at the conference was his Fourteen Points which had been instrumental in securing the armistice. Key among these was freedom of the seas, equality of trade, arms limitation, self-determination of peoples, and the formation of the League of Nations to mediate future disputes. Believing that he had an obligation to be a prominent figure at the conference, Wilson endeavored to create a more open and liberal world where democracy and liberty would be respected. French Concerns for the Conference While Wilson sought a softer peace for Germany, Clemenceau and the French wished to permanently weaken their neighbor economically and militarily. In addition to the return of Alsace-Lorraine, which had been taken by Germany following the Franco-Prussian War (1870-1871), Clemenceau argued in favor of heavy war reparations and the separation of the Rhineland to create buffer state between France and Germany. Furthermore, Clemenceau sought British and American assurances of aid should Germany ever attack France. The British Approach While Lloyd George supported the need for war reparations, his goals for the conference were more specific than his American and French allies. Concerned first and foremost for the preservation of the British Empire, Lloyd George sought to settle territorial issues, ensure the security of France, and remove the threat of the German High Seas Fleet. While he favored the formation of the League of Nations, he discouraged Wilsons call for self-determination as it could adversely affect Britains colonies. Italys Goals The weakest of the four major victorious powers, Italy sought to ensure that it received the territory that it had been promised by the Treaty of London in 1915. This largely consisted of the Trentino, Tyrol (including Istria and Trieste), and the Dalmatian coast excluding Fiume. Heavy Italian losses and a severe budget deficit as a result of the war led to a belief that these concessions had been earned. During the talks in Paris, Orlando was constantly hampered by his inability to speak English. The Negotiations For the early part of the conference, many of the key decisions were made by the Council of Ten which was comprised of the leaders and foreign ministers of the United States, Britain, France, Italy, and Japan. In March, it was decided that this body was too unwieldy to be effective. As a result, many of the foreign ministers and nations left conference, with talks continuing between Wilson, Lloyd George, Clemenceau, and Orlando. Key among the departures was Japan, whose emissaries were angered by a lack of respect and the conferences unwillingness to adopt a racial equality clause for the Covenant of the League of Nations. The group shrank further when the Italy was offered Trentino to the Brenner, the Dalmatian port of Zara, the island of Lagosta, and a few small German colonies in lieu of what was originally promised. Irate over this and the groups unwillingness to give Italy Fiume, Orlando departed Paris and returned home. As the talks progressed, Wilson was increasingly unable to garner acceptance of his Fourteen Points. In an effort to appease the American leader, Lloyd George and Clemenceau consented to the formation of the League of Nations. With several of the participants goals conflicting, the talks moved slowly and ultimately produced a treaty which failed to please any of the nations involved. On April 29, a German delegation, led by Foreign Minister Ulrich Graf von Brockdorff-Rantzau, was summoned to Versailles to receive the treaty. Upon learning of the content, the Germans protested that they had not been allowed to participate in the talks. Deeming the treatys terms a violation of honor, they withdrew from the proceedings. Terms of the Treaty of Versailles The conditions imposed upon Germany by the Treaty of Versailles were severe and wide-ranging. Germanys military was to be limited to 100,000 men, while the once formidable Kaiserliche Marine was reduced to no more than six battleships (not to exceed 10,000 tons), 6 cruisers, 6 destroyers, and 12 torpedo boats. In addition, production of military aircraft, tanks, armored cars, and poison gas was prohibited. Territorially, Alsace-Lorraine was returned to France, while numerous other changes reduced Germanys size. Key among these was the loss of West Prussia to the new nation of Poland while Danzig was made a free city to ensure Polish access to the sea. The province of Saarland was transferred to League of Nations control for a period of fifteen years. At the end of this period, a plebiscite was to determine whether it returned to Germany or was made part of France. Financially, Germany was issued a war reparations bill totaling  £6.6 billion (later reduced to  £4.49 billion in 1921). This number was determined by the Inter-Allied Reparations Commission. While Wilson took a more conciliatory view on this issue, Lloyd George had worked to increase the demanded amount. The reparations required by the treaty included not only money, but a variety of goods such as steel, coal, intellectual property, and agricultural produce. This mixed approach was an effort to prevent hyperinflation in postwar Germany which would decrease the value of the reparations. Several legal restrictions were also imposed, most notably Article 231 which laid sole responsibility for the war on Germany. A controversial part of the treaty, its inclusion had been opposed by Wilson and it became known as the War Guilt Clause. Part 1 of the treaty formed the Covenant of the League of Nations which was to govern the new international organization. German Reaction Signing In Germany, the treaty provoked universal outrage, particularly Article 231. Having concluded the armistice in expectation of a treaty embodying the Fourteen Points, Germans took to the streets in protest. Unwilling to sign it, the nations first democratically-elected chancellor, Philipp Scheidemann, resigned on June 20 forcing Gustav Bauer to form a new coalition government. Assessing his options, Bauer was soon informed that army was not capable of offering meaningful resistance. Lacking any other options, he dispatched Foreign Minister Hermann Mà ¼ller and Johannes Bell to Versailles. The treaty was signed in the Hall of Mirrors, where the German Empire had been proclaimed in 1871, on June 28. It was ratified by the National Assembly on July 9. Allied Reaction to the Treaty Upon release of the terms, many in France were displeased and believed that Germany had been treated too leniently. Among those who commented was Marshal Ferdinand Foch who predicted with eerie precision that This is not Peace. It is an Armistice for twenty years. As a result of their displeasure, Clemenceau was voted out of office in January 1920. While the treaty was better received in London, it ran into strong opposition in Washington. The Republican chairman of the Senate Foreign Relations Committee, Senator Henry Cabot Lodge, worked vigorously to block its ratification. Believing that Germany had been let off too easily, Lodge also opposed the United States participation in the League of Nations on constitutional grounds. As Wilson had intentionally excluded Republicans from his peace delegation and refused to consider Lodges changes to the treaty, the opposition found strong support in Congress. Despite Wilsons efforts and appeals to the public, the Senate voted against the tr eaty on November 19, 1919. The US formally made peace through the Knox-Porter Resolution which was passed in 1921. Though Wilsons League of Nations moved forward, it did so without American participation and never became an effective arbiter of world peace. The Map Changed While the Treaty of Versailles ended conflict with Germany, the Treaties of Saint-German and Trianon concluded the war with Austria and Hungary. With the collapse of the Austro-Hungarian Empire a wealth of new nations took shape in addition to the separation of Hungary and Austria. Key among these was Czechoslovakia and Yugoslavia. To the north, Poland emerged as an independent state as did Finland, Latvia, Estonia, and Lithuania. In the east, the Ottoman Empire made peace through the Treaties of Sà ¨vres and Lausanne. Long the sick man of Europe, the Ottoman Empire was reduced in size to Turkey, while France and Britain were given mandates over Syria, Mesopotamia, and Palestine. Having aided the aided in defeating the Ottomans, the Arabs were given their own state to the south. A Stab in the Back As the postwar Germany (Weimer Republic) moved forward, resentment over the end of the war and the Treaty of Versailles continued to fester. This coalesced in the stab-in-the back legend which stated that Germanys defeat was not the fault of the military but rather due to a lack of support at home from anti-war politicians and the sabotaging of the war effort by Jews, Socialists, and Bolsheviks. As such, these parties were seen to have stabbed the military in the back as it fought the Allies. The myth was given further credence by the fact that German forces had won the war on the Eastern Front and were still on French and Belgian soil when the armistice was signed. Resonating among conservatives, nationalists, and former-military, the concept became a powerful motivating force and was embraced by the emerging National Socialist Party (Nazis). This resentment, coupled with the economic collapse of Germany due to reparation-caused hyperinflation during the 1920s, facilitated the rise of the Nazis to power under Adolf Hitler. As such, the Treaty of Versailles may be seen as leading to many of the causes of World War II in Europe. As Foch had feared, the treaty simply served as a twenty-year armistice with World War II beginning in 1939.

Aftermath of World War 1 - Treaty of Versailles

Aftermath of World War 1 - Treaty of Versailles The World Comes to Paris In the wake of the November 11, 1918 armistice which ended hostilities on the Western Front, Allied leaders gathered in Paris to begin negotiations over the peace treaties that would formally conclude the war. Convening in the Salle de lHorloge at the French Foreign Ministry on January 18, 1919, the talks initially included leaders and representatives from over thirty nations. To this crowd was added a host of journalists and lobbyists from a variety of causes. While this unwieldy mass took part in the early meetings, it was President Woodrow Wilson of the United States, Prime Minister David Lloyd George of Britain, Prime Minister Georges Clemenceau of France, and Prime Minister Vittorio Orlando of Italy who came to dominate the talks. As defeated nations, Germany, Austria, and Hungary were prohibited from attending, as was Bolshevik Russia which was in the midst of a civil war. Wilsons Goals Arriving in Paris, Wilson became the first president to travel to Europe while in office. The basis for Wilsons position at the conference was his Fourteen Points which had been instrumental in securing the armistice. Key among these was freedom of the seas, equality of trade, arms limitation, self-determination of peoples, and the formation of the League of Nations to mediate future disputes. Believing that he had an obligation to be a prominent figure at the conference, Wilson endeavored to create a more open and liberal world where democracy and liberty would be respected. French Concerns for the Conference While Wilson sought a softer peace for Germany, Clemenceau and the French wished to permanently weaken their neighbor economically and militarily. In addition to the return of Alsace-Lorraine, which had been taken by Germany following the Franco-Prussian War (1870-1871), Clemenceau argued in favor of heavy war reparations and the separation of the Rhineland to create buffer state between France and Germany. Furthermore, Clemenceau sought British and American assurances of aid should Germany ever attack France. The British Approach While Lloyd George supported the need for war reparations, his goals for the conference were more specific than his American and French allies. Concerned first and foremost for the preservation of the British Empire, Lloyd George sought to settle territorial issues, ensure the security of France, and remove the threat of the German High Seas Fleet. While he favored the formation of the League of Nations, he discouraged Wilsons call for self-determination as it could adversely affect Britains colonies. Italys Goals The weakest of the four major victorious powers, Italy sought to ensure that it received the territory that it had been promised by the Treaty of London in 1915. This largely consisted of the Trentino, Tyrol (including Istria and Trieste), and the Dalmatian coast excluding Fiume. Heavy Italian losses and a severe budget deficit as a result of the war led to a belief that these concessions had been earned. During the talks in Paris, Orlando was constantly hampered by his inability to speak English. The Negotiations For the early part of the conference, many of the key decisions were made by the Council of Ten which was comprised of the leaders and foreign ministers of the United States, Britain, France, Italy, and Japan. In March, it was decided that this body was too unwieldy to be effective. As a result, many of the foreign ministers and nations left conference, with talks continuing between Wilson, Lloyd George, Clemenceau, and Orlando. Key among the departures was Japan, whose emissaries were angered by a lack of respect and the conferences unwillingness to adopt a racial equality clause for the Covenant of the League of Nations. The group shrank further when the Italy was offered Trentino to the Brenner, the Dalmatian port of Zara, the island of Lagosta, and a few small German colonies in lieu of what was originally promised. Irate over this and the groups unwillingness to give Italy Fiume, Orlando departed Paris and returned home. As the talks progressed, Wilson was increasingly unable to garner acceptance of his Fourteen Points. In an effort to appease the American leader, Lloyd George and Clemenceau consented to the formation of the League of Nations. With several of the participants goals conflicting, the talks moved slowly and ultimately produced a treaty which failed to please any of the nations involved. On April 29, a German delegation, led by Foreign Minister Ulrich Graf von Brockdorff-Rantzau, was summoned to Versailles to receive the treaty. Upon learning of the content, the Germans protested that they had not been allowed to participate in the talks. Deeming the treatys terms a violation of honor, they withdrew from the proceedings. Terms of the Treaty of Versailles The conditions imposed upon Germany by the Treaty of Versailles were severe and wide-ranging. Germanys military was to be limited to 100,000 men, while the once formidable Kaiserliche Marine was reduced to no more than six battleships (not to exceed 10,000 tons), 6 cruisers, 6 destroyers, and 12 torpedo boats. In addition, production of military aircraft, tanks, armored cars, and poison gas was prohibited. Territorially, Alsace-Lorraine was returned to France, while numerous other changes reduced Germanys size. Key among these was the loss of West Prussia to the new nation of Poland while Danzig was made a free city to ensure Polish access to the sea. The province of Saarland was transferred to League of Nations control for a period of fifteen years. At the end of this period, a plebiscite was to determine whether it returned to Germany or was made part of France. Financially, Germany was issued a war reparations bill totaling  £6.6 billion (later reduced to  £4.49 billion in 1921). This number was determined by the Inter-Allied Reparations Commission. While Wilson took a more conciliatory view on this issue, Lloyd George had worked to increase the demanded amount. The reparations required by the treaty included not only money, but a variety of goods such as steel, coal, intellectual property, and agricultural produce. This mixed approach was an effort to prevent hyperinflation in postwar Germany which would decrease the value of the reparations. Several legal restrictions were also imposed, most notably Article 231 which laid sole responsibility for the war on Germany. A controversial part of the treaty, its inclusion had been opposed by Wilson and it became known as the War Guilt Clause. Part 1 of the treaty formed the Covenant of the League of Nations which was to govern the new international organization. German Reaction Signing In Germany, the treaty provoked universal outrage, particularly Article 231. Having concluded the armistice in expectation of a treaty embodying the Fourteen Points, Germans took to the streets in protest. Unwilling to sign it, the nations first democratically-elected chancellor, Philipp Scheidemann, resigned on June 20 forcing Gustav Bauer to form a new coalition government. Assessing his options, Bauer was soon informed that army was not capable of offering meaningful resistance. Lacking any other options, he dispatched Foreign Minister Hermann Mà ¼ller and Johannes Bell to Versailles. The treaty was signed in the Hall of Mirrors, where the German Empire had been proclaimed in 1871, on June 28. It was ratified by the National Assembly on July 9. Allied Reaction to the Treaty Upon release of the terms, many in France were displeased and believed that Germany had been treated too leniently. Among those who commented was Marshal Ferdinand Foch who predicted with eerie precision that This is not Peace. It is an Armistice for twenty years. As a result of their displeasure, Clemenceau was voted out of office in January 1920. While the treaty was better received in London, it ran into strong opposition in Washington. The Republican chairman of the Senate Foreign Relations Committee, Senator Henry Cabot Lodge, worked vigorously to block its ratification. Believing that Germany had been let off too easily, Lodge also opposed the United States participation in the League of Nations on constitutional grounds. As Wilson had intentionally excluded Republicans from his peace delegation and refused to consider Lodges changes to the treaty, the opposition found strong support in Congress. Despite Wilsons efforts and appeals to the public, the Senate voted against the tr eaty on November 19, 1919. The US formally made peace through the Knox-Porter Resolution which was passed in 1921. Though Wilsons League of Nations moved forward, it did so without American participation and never became an effective arbiter of world peace. The Map Changed While the Treaty of Versailles ended conflict with Germany, the Treaties of Saint-German and Trianon concluded the war with Austria and Hungary. With the collapse of the Austro-Hungarian Empire a wealth of new nations took shape in addition to the separation of Hungary and Austria. Key among these was Czechoslovakia and Yugoslavia. To the north, Poland emerged as an independent state as did Finland, Latvia, Estonia, and Lithuania. In the east, the Ottoman Empire made peace through the Treaties of Sà ¨vres and Lausanne. Long the sick man of Europe, the Ottoman Empire was reduced in size to Turkey, while France and Britain were given mandates over Syria, Mesopotamia, and Palestine. Having aided the aided in defeating the Ottomans, the Arabs were given their own state to the south. A Stab in the Back As the postwar Germany (Weimer Republic) moved forward, resentment over the end of the war and the Treaty of Versailles continued to fester. This coalesced in the stab-in-the back legend which stated that Germanys defeat was not the fault of the military but rather due to a lack of support at home from anti-war politicians and the sabotaging of the war effort by Jews, Socialists, and Bolsheviks. As such, these parties were seen to have stabbed the military in the back as it fought the Allies. The myth was given further credence by the fact that German forces had won the war on the Eastern Front and were still on French and Belgian soil when the armistice was signed. Resonating among conservatives, nationalists, and former-military, the concept became a powerful motivating force and was embraced by the emerging National Socialist Party (Nazis). This resentment, coupled with the economic collapse of Germany due to reparation-caused hyperinflation during the 1920s, facilitated the rise of the Nazis to power under Adolf Hitler. As such, the Treaty of Versailles may be seen as leading to many of the causes of World War II in Europe. As Foch had feared, the treaty simply served as a twenty-year armistice with World War II beginning in 1939.

Research Based Argument - The Necessity of Capital Punishment Essay

Research Based Argument - The Necessity of Capital Punishment - Essay Example The stunning revelation in the article is that in the State of California, the annual legal costs related to capital punishment are estimated at $184 million. Also, it is claimed that by replacing death penalty with life sentences, this amount can be brought down to just $ 11.5 million. Admittedly, this claim Fagan makes seems attractive only to some hardcore do-gooders. People with a sane mind will easily identify that the lives of the citizens in a country cannot be put into jeopardy for economic benefits. It can be admitted that capital punishment invites extensive legal jargons in the forms of appeals and reviews. However, one has to remember the fact that this delay and higher expenditure only shows the ineffectiveness of our legal system; not the ineffectiveness of capital punishment. So, it is evidently irrational to set serial killers free to save the money spent on legal works. Also, as Nugent argues, locking up such insane shooters in jails for the rest of their lifetime wi ll cost taxpayers millions of dollars. One is forced to think whether it would not be a better administration of justice if the killer is executed and this millions of dollars are paid as compensation to the next of kin of the victims. Moreover, as Nugent points out, it costs only ‘a 25 cent bullet’ to eliminate the criminal in cases like the Tucson shootout. If any money more than that is spent on legal battles, it is the justice system to be blamed; not capital punishment. Also, the figures put forward by Fagan are under criticism for lack of evidence. In fact, the work ‘Death penalty and sentencing information’ by Sharp points out that life without parole (LWOP) is nearly $1.2 to $3.6 million more expensive than death penalty. Another minor argument seen in the article of Fagan is that sometimes the society seems as guilty as the culprit in certain crimes. For example, the killer of a 22 year old female is found to be mentally unstable and brain-damaged. The investigation proves that the killer had a very horrible upbringing as a child as he had his birth as an impoverished Mono tribe American Indian. Also, he was taken away from his alcoholic parents at a very early age and was molested and abused in foster homes and other institutions. As a result, he was addicted to heroin and other drugs by the time he turned 5. Thus, Fagan argues that in such cases, giving capital punishment to the criminal is unjustifiable as the culprit is not guiltier than the family and society he lives in. It is with this insight that the article says that if capital punishment is replaced with life imprisonment, â€Å"you would also run no chance of executing an innocent person† (Fagan). However, the fact is that laymen or the citizens of a country cannot bear the brunt of setting mentally deranged people free. For example, Nugent writes in The Washington Times about the Tucson shootout which killed six and wounded 13. As Fagan argues in his artic le, in this case too, the culprit was mentally deranged. As a result, he is going to spend the rest of his life in the comfort of jail eating up the tax paid by obedient citizens. As Nugent argues, â€Å"you don’t need to be an overpaid prison psychologist to determine that (the criminal is mentally deranged) no

E-learning across mobile platform applications (m-learning) Thesis Proposal

E-learning across mobile platform applications (m-learning) - Thesis Proposal Example Mobiles are playing an important role in learning process characterized by their ability to incorporate transportable devices used in the learning process. Since several years, usage of m-learning technologies for teaching and learning purposes has been increasing across the globe, and technology development made m-learning is an accessible tool evens for the physically challenged people (Kiernan, & Aizawa, 2004). Using mobile technology for deaf language is really invaluable, and can improve learners’ learning and communication capacity, but is not economical for poor and developing countries. In addition, texting in a foreign language may be difficult if people who are deaf having limited English ( Thornton, & Houser, 2005). For technicians also it a challenging task as they have to keep up their skill for the requirements of the growing market. They have to provide technical support for hands on practice whenever needs, and trained children. It burdens more on the company as it has to invest money for the research purpose. It has an intention of guiding, and providing an opportunity for hearing impaired students to improve their learning, and communication experiences using mobile technology. At the same time creation of mobile environment for social interactions where students are able to follow the content through their personal digital assistants without affecting time and place. Generally, students with hearing loss would face great difficulty in acquiring languages, and they have to use aid for hearing. They may face problems while understanding the speech of others and at the same time achieving effective communication through speaking or using signs may not be sufficient for them (Garcia Cabrere, 2002). So, for acquiring academic and intellectual skills, there is a necessity of developing reading and writing dimensions of oral communication effectively. For the purpose, there is a need for new