Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 11 - Section 11.4 - Partial Sums of Arithmetic and Geometric Sequences - Exercise Set: 4

Answer

$S_{8} = 85 $

Work Step by Step

Given geometric sequence $-1,2,-4,...$ $a_{1} = -1$ Common ratio $r = \frac{a_{n}}{a_{n-1}}$ $r= \frac{a_{2}}{a_{1}} = \frac{2}{-1} = -2$ Sum of first eight terms is $S_{8} = \frac{-1(1-(-2)^{8})}{1-(-2)}$ [Using $S_{n} =\frac{ a_{1}(1-r^{n})}{1-r}$] $S_{8} = \frac{-1(1-256)}{1+2} $ $S_{8} = \frac{-1(-255)}{3} $ $S_{8} = \frac{255}{3} $ $S_{8} = 85 $
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