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: 48

Answer

General Formula: $a_n=-70+(n-1)(-5)$ $a_{20}=-165$

Work Step by Step

The formula for the general term (the nth term) of an arithmetic sequence is: $a_n=a_1+(nāˆ’1)d$ where d = common difference $a_1$ = first term $a_n$ = nth term n = term number The given arithmetic sequence has: $a_1=-70$ and $d=-5$ Substitute these into the given formula above: $a_n = -70+ (n-1)(-5)$ Thus, $a_{20} = -70+(20-1)(-5) \\a_{20}=-70+19(-5) \\a_{20}=-70+(-95) \\a_{20}=-165$
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