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 796: 58


$\displaystyle \sum_{n=1}^{8}5(-\frac{5}{2})^{n-1}=-\frac{278835}{128}$

Work Step by Step

$\displaystyle \sum_{n=1}^{8}5(-\frac{5}{2})^{n-1}=5(-\frac{5}{2})^0+5(-\frac{5}{2})^1+...+5(-\frac{5}{2})^7$ $a_1=5(-\frac{5}{2})^0=5$ $r=\frac{a_2}{a_1}=\frac{5(-\frac{5}{2})^1}{5(-\frac{5}{2})^0}=-\frac{5}{2}$ $S_{6}=a_1(\frac{1-r^n}{1-r})=5(\frac{1-(-\frac{5}{2})^{8}}{1-(-\frac{5}{2})})=5·\frac{1-\frac{390625}{256}}{\frac{7}{2}}= 5·\frac{-\frac{390369}{256}}{\frac{7}{2}}=-\frac{278835}{128}$
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