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A sequence is periodic if the terms repeat in a cycle; Q + = Q for some k, which is known as the order of the sequence. e.g. -3, 1, -3, 1, -3, … is periodic with order 2. An arithmetic sequence is one where there is a common difference between each term.
The Sequences and Series Cheat Sheet is a document that provides a concise summary of key concepts, formulas, and techniques related to sequences and series in mathematics.
It also examines sequences and series in general, quick methods of writing them down, and techniques for investigating their behaviour. Legend has it that the inventor of the game called chess was told to name his own reward.
n!1. techniques for taking limits that you learned in Calc 1 and this class could come into play here so you might want to brush up on some examples from the lecture notes and homework. Series. So, in a sequence, we had a list of numbers. 1; 2; 3; 4; 5; 6; In a series, we have something similar.
A sequence is simply an ordered list u1, u2, u3,K, un, of numbers (or terms). This is often abbreviated to {}un. For our purposes each term un is usually given in one of two ways: (i) as a function of the preceding term(s), or (ii) as a function of its position in the sequence.
An explicit formula for this arithmetic sequence is given by an = a + (n −1)b, n ∈ N, a recursive formula is given by a1 = a and an = an−1 + b for n > 1. Here are some examples of arithmetic sequences, see if you can determine a and b in each case: 1, 2, 3, 4, 5, ... 2, 4, 6, 8, 10, ... 1, 4, 7, 10, 13, ...
13 SEQUENCES AND SERIES. Objectives. After studying this chapter you should. • be able to recognise geometric and arithmetic sequences; • understand å notation for sums of series; • be familiar with the standard formulas for å r, å r2 and å r3; 13.0 Introduction. Suppose you go on a sponsored walk. In the first hour you walk.
