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: 55

Answer

$S_7=-645$

Work Step by Step

We are asked to find the sum of: $-15+30-60+\cdots-960$ This is a geometric sequence with $a_1=-15$. We find $r$: $r=\frac{30}{-15}=-2$ We know that a geometric sequence has the form: $a_{n}=ar^{n-1}$ We use this to find the number of terms: $a_n=(-15)(-2)^{n-1}=-960$ $64=(-2)^{n-1}=\frac{(-2)^n}{-2}$ $-128=(-2)^n$ We see that $n$ must be odd: $128=2^n$ $n=\log_2 128$ $n=7$ We know the partial sum of a geometric sequence is: $S_n=a_1\frac{1-r^n}{1-r}$ Thus: $S_{7}=-15 \frac{1-(-2)^{7}}{1-(-2)}=-645$
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