Calculus with Applications (10th Edition)

Published by Pearson

Chapter 12 - Sequences and Series - 12.1 Geometric Sequences - 12.1 Exercises - Page 612: 27

Answer

$${S_5} = 33$$

Work Step by Step

\eqalign{ & {\text{the sum of the first }}n{\text{ terms of a geometric sequence}}{\text{ is given by}} \cr & {S_n} = \frac{{{a_1}\left( {{r^n} - 1} \right)}}{{r - 1}},{\text{ where }}r \ne 1 \cr & {\text{let }}n = 5,\,\,\,{a_1} = 3{\text{ and }}r = - 2 \cr & {S_5} = \frac{{\left( 3 \right)\left( {{{\left( { - 2} \right)}^5} - 1} \right)}}{{ - 2 - 1}} \cr & {\text{simplifying}} \cr & {S_5} = \frac{{\left( 3 \right)\left( { - 33} \right)}}{{ - 3}} \cr & {S_5} = 33 \cr}

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