![]() ![]() The fixed number is called a common difference (d) of the AP. And hence, we define the general term and it is denoted by a n.or t n.įor the above example, a n = 2n, where n is Integer.Īn arithmetic progression is a sequence whose terms increase or decrease by a fixed number. We want a more compact way to show how each term is defined. Often when working with sequences we do not want to write out all the terms. A sequence containing a finite number of terms is called a finite sequence and a sequence is called infinite if it is not a finite sequence. The numbers or objects are also known as the terms of the sequence. Well, all the answers to these questions you will able to tell when you study Sequences and Series.Īfter reading this chapter you will be able to:įind a formula for the general term (nth term) of a sequenceĪ sequence is an arrangement of a list of objects or numbers in a definite order. So now you tell me, What will be the total number of grains? How much time does craftsman require to complete the count? The amount of rice that craftsman asked, will that be available on our planet? "Oh, that won't be required," said the craftsman. "But before you receive the grains of rice, just to be sure you are getting what you asked for, I'd like you to count each and every grain I give you." By the 21st square he owed over a million grains of rice by the 41st, it was over a trillion grains of rice - more rice than he, his subjects or any emperor anywhere could afford in the world.Īfter all, he was the emperor. In the second row, things got out of control. by the end of the first row, he was up to 128 grains. The first few squares on the board cost the emperor 1 grain, then 2, then 4. Well, that turned out to be more than a little difficult. And he ordered his treasurer to pay the craftsman for the chessboard. "Well, I can do that," said the emperor, not thinking much. "All I want," said the craftsman, "is for you to put a single grain of rice on the first square, two grains on the second square, four on the third square, eight on the fourth square, and so on and so on for all 64 squares, with each square having double the number of grains as the square before." The emperor agreed, amazed that the man had asked for such a small reward ![]() "Your Highness, I don't want money for this. Crack JEE 2021 with JEE/NEET Online Preparation Program Start Now ![]()
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