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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, ...
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.
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.
6.2.1 Introduction. If an is a sequence, the di erence between consecutive terms is an+1 an. If there exists a constant such that = an+1 an for all n then an is called an arithmetic sequence. The number is called the common di erence of the arithmetic sequence.
There are two major types of sequence, arithmetic and geometric. This section will consider arithmetic sequences (also known as arithmetic progressions, or simply A.P). The characteristic of such a sequence is that there is a common difference between successive terms. For example: 1, 3, 5, 7, 9, 11, . . .
Write the recursive formula for each sequence. 35) 2, 4, 7, 11 , 16 , ... a n = a n − 1 + n a 1 = 2 36) 15 , 215 , 415 , 615 , 815 , ... a n = a n − 1 + 200 a 1 = 15-2-Create your own worksheets like this one with Infinite Algebra 2. Free trial available at KutaSoftware.com. Title: Introduction to Sequences
By Fourier series, certain functions can be represented as an infinite sum of trigonometric functions. Using infinite series, differential equations in problems of signal transmission, chemical diffusion, vibration and heat flow can be solved and non elementary integrals evaluated.
