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: 57


$\displaystyle \sum_{n=1}^{6}(-7)^{n-1}=-14706$

Work Step by Step

$\displaystyle \sum_{n=1}^{6}(-7)^{n-1}=(-7)^0+(-7)^1+...+(-7)^5$ $a_1=(-7)^0=1$ $r=\frac{a_2}{a_1}=\frac{(-7)^1}{(-7)^0}=-7$ $S_{6}=a_1(\frac{1-r^n}{1-r})=1(\frac{1-(-7)^{6}}{1-(-7)})=\frac{1-117649}{8}=-14706$
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