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: 55


$\displaystyle \sum_{n=1}^{7}4^{n-1}=5461$

Work Step by Step

$\displaystyle \sum_{n=1}^{7}4^{n-1}=4^0+4^1+...+4^6$ $a_1=4^0=1$ $r=\frac{a_2}{a_1}=\frac{4^1}{4^0}=4$ $S_7=a_1(\frac{1-r^n}{1-r})=1(\frac{1-4^7}{1-4})=\frac{-16383}{-3}=5461$
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