Algebra and Trigonometry 10th Edition

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

Chapter 11 - 11.3 - Geometric Sequences and Series - 11.3 Exercises - Page 795: 20


$a_1=4$ $a_2=-2\sqrt 2$ $a_3=2$ $a_4=-\sqrt 2$ $a_5=1$

Work Step by Step

$a_n=a_1r^{n-1}$ $a_1=4,~~r=-\frac{1}{\sqrt 2}$ $a_2=4(-\frac{1}{\sqrt 2})^{2-1}=4(-\frac{1}{\sqrt 2})=-\frac{4}{\sqrt 2}=-\frac{4}{\sqrt 2}\frac{\sqrt 2}{\sqrt 2}=-\frac{4\sqrt 2}{2}=-2\sqrt 2$ $a_3=4(-\frac{1}{\sqrt 2})^{3-1}=4(-\frac{1}{\sqrt 2})^2=4.\frac{1}{2}=2$ $a_4=4(-\frac{1}{\sqrt 2})^{3-1}=4(-\frac{1}{\sqrt 2})^3=-\frac{4}{2\sqrt 2}=-\frac{2}{\sqrt 2}\frac{\sqrt 2}{\sqrt 2}=-\frac{2\sqrt 2}{2}=-\sqrt 2$ $a_5=4(-\frac{1}{\sqrt 2})^{5-1}=4(-\frac{1}{\sqrt 2})^4=4.\frac{1}{4}=1$
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