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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, ...
This unit introduces sequences and series, and gives some simple examples of each. It also explores particular types of sequence known as arithmetic progressions (APs) and geometric progressions (GPs), and the corresponding series.
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.
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.
n is a sequence, the di erence between consecutive terms is a n+1 a n. If there exists a constant ˝ such that ˝= a n+1 a n for all nthen a n is called an arithmetic sequence. The number ˝is called the common di erence of the arithmetic sequence. Example 1 Determine whether the sequences are arithmetic. If so, nd the common di erence. a) 4;7 ...
There are 3 ways to express a sequence: 1. list all the terms 2. a function f : Z+!R such that a n = f(n) 3. an inductive formula. Chapter 11: Sequences and Series, Section 11.1 Sequences7 / 1
Sequences. Sequences are just ordered lists of numbers such as this one. f1; 2; 3; 4; 5; g. We label each term with an index so we can keep track of it. We’ll call the first term a1, the second term a2, and so on. So we would notate the general n th term as an.
