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: 33

Answer

$10230$

Work Step by Step

$5\times 2^{1} + 5\times 2^{2} + 5\times 2^{3} + ................+ 5\times 2^{10}$ First term $a_{1}= 10$ and common ratio $r = 2$ Sum of the first $n$ terms of Geometric sequence is $S_{n}= \frac{a_{1}(1-r^{n})}{1-r}$ Substituting $a_{1}= 10, r = 2$ and $n=10$ $S_{n}= \frac{a_{1}(1-r^{n})}{1-r}$ $S_{10}= \frac{10(1-2^{10})}{1-2}$ $S_{10}= \frac{10(1-1024)}{-1}$ $S_{10}= \frac{10(-1023)}{-1}$ $S_{10}= 10230$
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