Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 5 - Number Theory and the Real Number System - 5.7 Arithmetic and Geometric Sequences - Exercise Set 5.7: 43

Answer

General Formula: $a_n=7+(n-1)(-4)$ $a_{20}=-69$

Work Step by Step

The formula for the general term (the nth term) of an arithmetic sequence is: $a_n=a_1 + (n-1)d$ where d = common difference $a_1$ = first term $a_n$ = nth term n = term number To find the formula for the general term, perform the following steps: (1) Find the values of $a_1$ and $d$ The given sequence has: $a_1 =7$ $d= 3 -7 = -4$ (2) Substitute the values of $a_1$ and $d$ in the general formula given above to find: $a_n= 7 + (n-1)(-4)$ Therefore, the 20th term of the sequence is: $a_{20} = 7+ (20-1)(-4) \\a_{20} = 7+19(-4) \\a_{20} = 7 + (-76) \\a_{20} = -69$
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