College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 8, Sequences and Series - Section 8.3 - Geometric Sequences - 8.3 Exercises: 57

Answer

$S_{8}=13,888,888.75$

Work Step by Step

We are asked to find the sum of: $1.25+12.5+125+\cdots+12,500,000$ We see that this is a geometric sequence with $a_1=1.25$. We find $r$: $r=12.5/1.25=10$ We know that a geometric sequence has the form: $a_{n}=ar^{n-1}$ We use this to find $n$: $a_n=(1.25)(10)^{n-1}$ $12500000=(1.25)(10)^{n-1}$ $10000000=(10)^{n-1}$ $n-1=7$ $n=8$ We know the partial sum of a geometric sequence is: $S_n=a_1\frac{1-r^n}{1-r}$ $S_{8}=1.25 \frac{1-10^{8}}{1-10}=13,888,888.75$
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