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: 49

Answer

$S_6 = 315$

Work Step by Step

RECALL: The partial sum $S_n$ (sum of the first $n$ terms) of a geometric sequence is given by the formula: $S_n=a\left(\dfrac{1-r^n}{1-r}\right), r\ne 1$ where $a$ = first term $r$ = common ratio The given geometric sequence has: $a=5 \\r=2$ Thus, the sum of the first 6 terms is equal to: $S_6 =5\left(\dfrac{1-2^6}{1-2}\right) \\S_6=5\left(\dfrac{1-64}{-1}\right) \\S_6=5 \left(\dfrac{-63}{-1}\right) \\S_6=5(63) \\S_6 = 315$
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