Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 11 - Review Exercises - Page 841: 49


$a_n=-36(-\frac{1}{2})^n$ $a_1=18$ $a_2=-9$ $a_3=\frac{9}{2}$ $a_4=-\frac{9}{4}$ $a_5=\frac{9}{8}$

Work Step by Step

$a_1=18,~~a_2=-9$ $r=\frac{a_2}{a_1}=\frac{-9}{18}=-\frac{1}{2}$ The nth term of a geometric sequence: $a_n=a_1r^{n-1}$ $a_n=18(-\frac{1}{2})^{n-1}=18(-\frac{1}{2})^n(-\frac{1}{2})^{-1}=18(-2)(-\frac{1}{2})^n=-36(-\frac{1}{2})^n$ $a_3=-36(-\frac{1}{2})^3=-36(-\frac{1}{8})=\frac{9}{2}$ $a_4=-36(-\frac{1}{2})^4=-36(\frac{1}{16})=-\frac{9}{4}$ $a_5=-36(-\frac{1}{2})^5=-36(-\frac{1}{32})=\frac{9}{8}$
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