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 797: 92b

Answer

See below

Work Step by Step

An infinite geometric series converges if and only if $|r|\lt1$, where $r$ is the common ratio. If it converges, then it equals $\frac{a_1}{1-r}$ where $a_1$ is the first term. Here only $r=0.75$ has an absolute value less than $1$, thus the series that can be summed up is $a_n=20(0.75)^{n-1}$
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