Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 12 Sequences and Series - 12.3 Analyze Geometric Sequences and Series - Guided Practice for Examples 2, 3, and 4 - Page 812: 6


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Work Step by Step

The nth term of a geometric series can be obtained by the following formula: $a_n=a_1\cdot r^{n-1}$, where $a_1$ is the first term and $r$ is the common ratio. Here the common ratio is $5$ and $a_1=3$. Hence here: $a_4/a_2=r^2$, thus $r=0.5$, $a_2=a_1\cdot0.5^{2-1}$, thus $a_1=-12$, hence $a_n=-12\cdot(0.5)^{n-1}$, thus $a_8=-12\cdot(0.5)^{8-1}=-0.09375$
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