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: 46


for $r=\sqrt 6$: $a_1=2$ $a_2=2\sqrt 6$ $a_3=12$ $a_4=12\sqrt 6$ $a_5=72$ for $r=-\sqrt 6$: $a_1=2$ $a_2=-2\sqrt 6$ $a_3=12$ $a_4=-12\sqrt 6$ $a_5=72$

Work Step by Step

$a_1=2,~~a_3=12$ The nth term of a geometric sequence: $a_n=a_1r^{n-1}$ $a_3=a_1r^{3-1}$ $12=2r^2$ $6=r^2$ $r=\sqrt 6$ or $r=-\sqrt 6$ for $r=\sqrt 6$: $a_2=a_1r^{2-1}=2\sqrt 6$ $a_3=12$ $a_4=a_1r^{4-1}=2(\sqrt 6)^3=2(6\sqrt 6)=12\sqrt 6$ $a_5=a_1r^{5-1}=2(\sqrt 6)^4=2(36)=72$ for $r=-\sqrt 6$: $a_2=a_1r^{2-1}=2(-\sqrt 6)=-2\sqrt 6$ $a_3=12$ $a_4=a_1r^{4-1}=2(-\sqrt 6)^3=2(-6\sqrt 6)=-12\sqrt 6$ $a_5=a_1r^{5-1}=2(-\sqrt 6)^4=2(36)=72$
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