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 - Page 658: 7


$S_{4} = \frac{312}{125} $

Work Step by Step

Given geometric sequence $2,\frac{2}{5},\frac{2}{25},...$ $a_{1} =2$ Common ratio $r = \frac{a_{n}}{a_{n-1}}$ $r= \frac{a_{2}}{a_{1}} = \frac{\frac{2}{5}}{2} = \frac{2}{5} \times \frac{1}{2} = \frac{1}{5}$ To find sum of first four terms, substitute $a_{1}, r $ and $n=4$ in $S_{n} =\frac{ a_{1}(1-r^{n})}{1-r}$ $S_{4} =\frac{2(1-(\frac{1}{5})^{4})}{1-(\frac{1}{5})}$ $S_{4} =\frac{2(1-\frac{1}{625})}{\frac{5-1}{5}}$ $S_{4} =\frac{2(\frac{625-1}{625})}{\frac{4}{5}}$ $S_{4} = 2 \times \frac{624}{625} \times \frac{5}{4}$ $S_{4} = \frac{312}{125} $
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