For a Fibonacci sequence, from the third term onwards, each term in the sequence is the sum of the previous two terms in that sequence. If the difference in squares of 7th and 6th terms of this sequence is 517, what is the 10th term of this sequence? ?->(Show Answer!)

1. For a Fibonacci sequence, from the third term onwards, each term in the sequence is the sum of the previous two terms in that sequence. If the difference in squares of 7th and 6th terms of this sequence is 517, what is the 10th term of this sequence?

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By: anil on 05 May 2019 02.31 am

It is given that in a Fibonacci sequence, from the third term on wards, each term in the sequence is the sum of the previous two terms in that sequence. Let x and y be the 1st and 2nd term respectively. 3rd term = x+y 4th term = x+2y 5th term = 2x+3y 6th term = 3x+5y 7th term = 5x+8y We know that difference of the squares of 6th and 7th terms is 517 = 47*11 . And $$a^2-b^2=(a+b)(a-b)$$. Applying above formula we get (8x+13y)(2x+3y) = 47*11. So only possible way is (8x+13y)=47 and 2x+3y=11 . Solving we get x=1 and y=3 . Using the concept that every term is the sum of the previous two terms, as used in the beginning of the solution, we get 10th term as 21x+34y, which gives 10th term as 123.

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MCQ-> The second plan to have to examine is that of giving to each person what she deserves. Many people, especially those who are comfortably off, think this is what happens at present: that the industrious and sober and thrifty are never in want, and that poverty is due to idleness, improvidence, drinking, betting, dishonesty, and bad character generally. They can point to the fact that a labour whose character is bad finds it more difficult to get employment than one whose character is good; that a farmer or country gentleman who gambles and bets heavily, and mortgages his land to live wastefully and extravagantly, is soon reduced to poverty; and that a man of business who is lazy and does not attend to it becomes bankrupt. But this proves nothing that you cannot eat your cake and have it too; it does not prove that your share of the cake was a fair one. It shows that certain vices make us rich. People who are hard, grasping, selfish, cruel, and always ready to take advantage of their neighbours, become very rich if they are clever enough not to overreach themselves. On the other hand, people who are generous, public spirited, friendly, and not always thinking of the main chance, stay poor when they are born poor unless they have extraordinary talents. Also as things are today, some are born poor and others are born with silver spoons in their mouths: that is to say, they are divided into rich and poor before they are old enough to have any character at all. The notion that our present system distributes wealth according to merit, even roughly, may be dismissed at once as ridiculous. Everyone can see that it generally has the contrary effect; it makes a few idle people very rich, and a great many hardworking people very poor.On this, intelligent Lady, your first thought may be that if wealth is not distributed according to merit, it ought to be; and that we should at once set to work to alter our laws so that in future the good people shall be rich in proportion to their goodness and the bad people poor in proportion to their badness. There are several objections to this; but the very first one settles the question for good and all. It is, that the proposal is impossible and impractical. How are you going to measure anyone's merit in money? Choose any pair of human beings you like, male or female, and see whether you can decide how much each of them should have on her or his merits. If you live in the country, take the village blacksmith and the village clergyman, or the village washerwoman and the village schoolmistress, to begin with. At present, the clergyman often gets less pay than the blacksmith; it is only in some villages he gets more. But never mind what they get at present: you are trying whether you can set up a new order of things in which each will get what he deserves. You need not fix a sum of money for them: all you have to do is to settle the proportion between them. Is the blacksmith to have as much as the clergyman? Or twice as much as the clergyman? Or half as much as the clergyman? Or how much more or less? It is no use saying that one ought to have more the other less; you must be prepared to say exactly how much more or less in calculable proportion.Well, think it out. The clergyman has had a college education; but that is not any merit on his part: he owns it to his father; so you cannot allow him anything for that. But through it he is able to read the New Testament in Greek; so that he can do something the blacksmith cannot do. On the other hand, the blacksmith can make a horse-shoe, which the parson cannot. How many verses of the Greek Testament are worth one horse-shoe? You have only to ask the silly question to see that nobody can answer it.Since measuring their merits is no use, why not try to measure their faults? Suppose the blacksmith swears a good deal, and gets drunk occasionally! Everybody in the village knows this; but the parson has to keep his faults to himself. His wife knows them; but she will not tell you what they are if she knows that you intend to cut off some of his pay for them. You know that as he is only a mortal human being, he must have some faults; but you cannot find them out. However, suppose he has some faults he is a snob; that he cares more for sport and fashionable society than for religion! Does that make him as bad as the blacksmith, or twice as bad, or twice and quarter as bad, or only half as bad? In other words, if the blacksmith is to have a shilling, is the parson to have six pence, or five pence and one-third, or two shillings? Clearly these are fools' questions: the moment they bring us down from moral generalities to business particulars it becomes plain to every sensible person that no relation can be established between human qualities, good or bad, and sums of money, large or small.It may seem scandalous that a prize-fighter, for hitting another prize-fighter so hard at Wembley that he fell down and could not rise within ten seconds, received the same sum that was paid to the Archbishop of Canterbury for acting as Primate of the Church of England for nine months; but none of those who cry out against the scandal can express any better in money the difference between the two. Not one of the persons who think that the prize-fighter should get less than the Archbishop can say how much less. What the prize- fighter got for his six or seven months' boxing would pay a judge's salary for two years; and we all agree that nothing could be more ridiculous, and that any system of distributing wealth which leads to such absurdities must be wrong. But to suppose that it could be changed by any possible calculation that an ounce of archbishop of three ounces of judge is worth a pound of prize-fighter would be sillier still. You can find out how many candles are worth a pound of butter in the market on any particular day; but when you try to estimate the worth of human souls the utmost you can say is that they are all of equal value before the throne of God:And that will not help you in the least to settle how much money they should have. You must simply give it up, and admit that distributing money according to merit is beyond mortal measurement and judgement.Which of the following is not a vice attributed to the poor by the rich?
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MCQ-> I want to stress this personal helplessness we are all stricken with in the face of a system that has passed beyond our knowledge and control. To bring it nearer home, I propose that we switch off from the big things like empires and their wars to more familiar little things. Take pins for example! I do not know why it is that I so seldom use a pin when my wife cannot get on without boxes of them at hand; but it is so; and I will therefore take pins as being for some reason specially important to women.There was a time when pinmakers would buy the material; shape it; make the head and the point; ornament it; and take it to the market, and sell it and the making required skill in several operations. They not only knew how the thing was done from beginning to end, but could do it all by themselves. But they could not afford to sell you a paper of pins for the farthing. Pins cost so much that a woman's dress allowance was calling pin money.By the end of the 18th century Adam Smith boasted that it took 18 men to make a pin, each man doing a little bit of the job and passing the pin on to the next, and none of them being able to make a whole pin or to buy the materials or to sell it when it was made. The most you could say for them was that at least they had some idea of how it was made, though they could not make it. Now as this meant that they were clearly less capable and knowledgeable men than the old pin-makers, you may ask why Adam Smith boasted of it as a triumph of civilisation when its effect had so clearly a degrading effect. The reason was that by setting each man to do just one little bit of the work and nothing but that, over and over again, he became very quick at it. The men, it is said, could turn out nearly 5000 pins a day each; and thus pins became plentiful and cheap. The country was supposed to be richer because it had more pins, though it had turned capable men into mere machines doing their work without intelligence and being fed by the spare food of the capitalist just as an engine is fed with coals and oil. That was why the poet Goldsmith, who was a farsighted economist as well as a poet, complained that 'wealth accumulates, and men decay'.Nowadays Adam Smith's 18 men are as extinct as the diplodocus. The 18 flesh-and-blood men have been replaced by machines of steel which spout out pins by the hundred million. Even sticking them into pink papers is done by machinery. The result is that with the exception of a few people who design the machines, nobody knows how to make a pin or how a pin is made: that is to say, the modern worker in pin manufacture need not be one-tenth so intelligent, skilful and accomplished as the old pinmaker; and the only compensation we have for this deterioration is that pins are so cheap that a single pin has no expressible value at all. Even with a big profit stuck on to the cost-price you can buy dozens for a farthing; and pins are so recklessly thrown away and wasted that verses have to be written to persuade children (without success) that it is a sin to steal, if even it’s a pin.Many serious thinkers, like John Ruskin and William Morris, have been greatly troubled by this, just as Goldsmith was, and have asked whether we really believe that it is an advance in wealth to lose our skill and degrade our workers for the sake of being able to waste pins by the ton. We shall see later on, when we come to consider the Distribution of Leisure, that the cure for this is not to go back to the old free for higher work than pin-making or the like. But in the meantime the fact remains that the workers are now not able to make anything themselves even in little bits. They are ignorant and helpless, and cannot lift their finger to begin their day's work until it has all been arranged for them by their employer's who themselves do not understand the machines they buy, and simply pay other people to set them going by carrying out the machine maker's directions.The same is true for clothes. Earlier the whole work of making clothes, from the shearing of the sheep to the turning out of the finished and washed garment ready to put on, had to be done in the country by the men and women of the household, especially the women; so that to this day an unmarried woman is called a spinster. 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The people engaged in the making of them know even less; for many of them are too poor to have much choice of materials when they buy their own clothes.Thus the capitalist system has produced an almost universal ignorance of how things are made and done, whilst at the same time it has caused them to be made and done on a gigantic scale. We have to buy books and encyclopaedias to find out what it is we are doing all day; and as the books are written by people who are not doing it, and who get their information from other books, what they tell us is twenty to fifty years out of date knowledge and almost impractical today. And of course most of us are too tired of our work when we come home to want to read about it; what we need is cinema to take our minds off it and feel our imagination.It is a funny place, this word of capitalism, with its astonishing spread of education and enlightenment. There stand the thousands of property owners and the millions of wage workers, none of them able to make anything, none of them knowing what to do until somebody tells them, none of them having the least notion of how it is made that they find people paying them money, and things in the shops to buy with it. And when they travel they are surprised to find that savages and Esquimaux and villagers who have to make everything for themselves are more intelligent and resourceful! The wonder would be if they were anything else. We should die of idiocy through disuse of our mental faculties if we did not fill our heads with romantic nonsense out of illustrated newspapers and novels and plays and films. Such stuff keeps us alive, but it falsifies everything for us so absurdly that it leaves us more or less dangerous lunatics in the real world.Excuse my going on like this; but as I am a writer of books and plays myself, I know the folly and peril of it better than you do. And when I see that this moment of our utmost ignorance and helplessness, delusion and folly, has been stumbled on by the blind forces of capitalism as the moment for giving votes to everybody, so that the few wise women are hopelessly overruled by the thousands whose political minds, as far as they can be said to have any political minds at all, have been formed in the cinema, I realise that I had better stop writing plays for a while to discuss political and social realities in this book with those who are intelligent enough to listen to me.A suitable title to the passage would be
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MCQ-> Please read the three reports (newspaper articles) on ranking of different players and products in smart phones industry and answer the questions that follow. Report 1: (Feb, 2013) Apple nabs crown as current top US mobile phone vendor Apple’s reign may not be long, as Samsung is poised to overtake Apple in April, 2013. For the first time since Apple entered the mobile phone market in 2007, it has been ranked the top mobile phone vendor in the US. For the latter quarter of 2012, sales of its iPhone accounted for 34 percent of all mobile phone sales in the US - including feature phones - according to the latest data from Strategy Analytics. While the iPhone has consistently been ranked the top smartphone sold in the US, market research firm NPD noted that feature phone sales have fallen off a cliff recently, to the point where 8 out of every 10 mobile phones sold in the US are now smartphones. 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In the US smartphone market, LG is fifth with 6 percent. Note how the percentages aren’t all that different from overall mobile phone market share - for all intents and purposes, the smartphone market is the mobile phone market in the US going forward. Still, Samsung was the top mobile phone vendor overall for 2012, and Strategy Analytics expects Samsung to be back on top soon. “Samsung had been the number one mobile phone vendor in the US since 2008, and it will surely be keen to recapture that title in 2013 by launching improved new models such as the rumored Galaxy S4”. And while Apple is the top vendor overall among smartphones, its iOS platform is still second to the Android platform overall. Samsung is the largest vendor selling Android-based smartphones, but Motorola, HTC, LG, and others also sell Android devices, giving the platform a clear advantage over iOS both domestically and globally. Report 2: Reader’s Response (2013, Feb) I don’t actually believe the numbers for Samsung. Ever since the debacle in early 2011, when Lenovo called into question the numbers Samsung was touting for tablet shipments, stating that Samsung had only sold 20,000 of the 1.5 million tablets they shipped into the US the last quarter of 2010, Samsung (who had no response to Lenovo) has refused to supply quarterly sales numbers for smartphones or tablets. That’s an indication that their sales aren’t what analysts are saying. We can look to several things to help understand why. In the lawsuit between Apple and Samsung here last year, both were required to supply real sales numbers for devices under contention. The phones listed turned out to have sales between one third and one half of what had been guessed by IDC and others. Tablet sales were even worse. Of the 1.5 million tablets supposedly shipped to the US during that time, only 38,000 were sold. Then we have the usage numbers. Samsung tablets have only a 1.5% usage rate, where the iPad has over 90%. Not as much a difference with the phones but it’s still overwhelmingly in favor of iPhone. The problem is that with Apple’s sales, we have actual numbers to go by. The companies who estimate can calibrate what they do after those numbers come out. But with Samsung and many others, they can’t ever calibrate their methods, as there are no confirming numbers released from the firms. A few quarters ago, as a result, we saw iSupply estimate Samsung’s smartphone sales for the quarter at 32 million, with estimates from others all over the place up to 50 million. Each time some other company reported a higher number for that same quarter, the press dutifully used that higher number as THE ONE. But none of them was the one. Without accurate self-reporting of actual sales to the end users, none of these market share charts are worth a damn! Report 3: Contradictory survey (Feb, 2013) iPhone5 Ranks Fifth In U.S. Customer Satisfaction Survey inShare. The iPhone5 ranks fifth in customer satisfaction according to the results of a recent survey from OnDevice Research, a mobile device research group. In the poll, they asked 320,000 smartphone and tablet users from six different countries, how satisfied they were with their devices. According to 93,825 people from the US, Motorola Atrix HD is the most satisfying and Motorola’s Droid Razr took second spot. HTC Corp (TPE : 2498)’s Rezound 4G and Samsung Galaxy Note 2 took third and fourth spots, while Apple’s iPhone5 landed in fifth spot. It appears that Apple may be lagging in consumer interest. OnDevice Research, Sarah Quinn explained, “Although Apple created one of the most revolutionary devices of the past decade, other manufactures have caught up, with some Android powered devices now commanding higher levels of user satisfaction.” Despite the lower rankings, things aren’t looking too bad for Apple Inc. (NASDAQ:AAPL) elsewhere. In the United Kingdom, they ranked second place, right after HTC One X. Interesting enough, Apple did take top spot for overall satisfaction of mobile device, whereas Google Inc. (NASDAQ:GOOG) ranked second. Motorola Mobility Holdings Inc. (NYSE:NOK) took third, fourth, and fifth places respectively, while Sony Ericsson trailed behind at sixth place. The survey sampled mobile device users in the following countries: United States, United Kingdom, France, Germany, Japan, and Indonesia. Although OnDevice didn’t share the full list of devices mentioned in the survey, it does show some insight to what customers want. Unfortunately, there were still many questions regarding the survey that were left unanswered. Everyone wants to know why Google Inc. (NASDAQ:GOOG) was on the list when they are not an actual smartphone maker and why was Samsung Electronics Co., Ltd. (LON:BC94) on the bottom of the satisfaction list when the brand is leading elsewhere.

Source: 92.825 US mobile users, July 2012 - January 2013 Fortunately, those questions were answered by OnDevice Research’s representative. He explained that the survey was conducted on mobile web where the survey software could detect the taker’s device and since user’s rate their satisfaction levels on a 1 to 10 scale, thanks to the Nexus device, Google was included.If you analyze the three reports above, which of the following statements would be the best inference?
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