College Algebra 7th Edition

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

Chapter 8, Sequences and Series - Section 8.2 - Arithmetic Sequences - 8.2 Exercises: 53

Answer

$S_{15}=870$

Work Step by Step

RECALL: The sum of the first $n$ terms ($S_n$) of an arithmetic sequence is given by the formula: $S_n=\dfrac{n}{2}\left[2a+(n-1)d\right]$ where $a$ = first term $d$ = common difference The given arithmetic sequence has: $a=-40 \\d=14$ Thus, to find the sum of the first 15 terms, substitute the given values to the formula above to obtain: $S_n=\dfrac{n}{2}[2a+(n-1)d] \\S_{15}=\dfrac{15}{2}[2(-40) + (15-1)(14)] \\S_{15}=\dfrac{15}{2}[-80+14(14)] \\S_{15}=\dfrac{15}{2}(-80+196) \\S_{15}=\dfrac{15}{2}(116) \\S_{15}=870$
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