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 - Page 330: 87


$a_{40}=-1.819 \times 10^{-9}$

Work Step by Step

The nth term of a geometric sequence can be found using the formula: $a_n=a_1(r^{n-1})$ where r= common ratio $a_1$ = first term $a_n$ = nth term n = term number Substitute the given values of $a_1$, n, and $r$ to find: $a_{40}=1000(-\frac{1}{2})^{40-1} \\a_{40}=1000(-\frac{1}{2})^{39} \\a_{40}=-1.818989404 \times 10^{-9}$
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