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 - 12.3 Exercises - Skill Practice - Page 814: 25


$a_n=5(-\dfrac{14}{5})^{n-1}$ and $a_7= 2409.45$

Work Step by Step

The given series shows a geometric series with a common ratio $5r=-14 $ Thus, $r=-\dfrac{14}{5}$ The nth term is given by $a_n= a_1 r^{n-1}$ This gives: $a_n=5(-\dfrac{14}{5})^{n-1}$ Plug in $n=7$ $a_7=5(-\dfrac{14}{5})^{7-1} \approx 2409.45$ Hence, $a_n=5(-\dfrac{14}{5})^{n-1}$ and $a_7= 2409.45$
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