College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 8 - Sequences, Induction, and Probability - Exercise Set 8.3 - Page 742: 109



Work Step by Step

The total flies($20000$) can be represented by the sum of the infinite geometric series with first term $a_1$ and common ratio $r=0.9$. 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 $0.9\lt1$. Hence the sum: $20000=\dfrac{a_1}{1-0.9}\\20000=\dfrac{a_1}{0.1}\\20000=10a_1\\2000=a_1$ Thus the answer is $2000$
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