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: 52

Answer

$S_{30}=-3180$

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: $a=10 \\d=-8$ Thus, to find the sum of the first 30 terms, substitute the given values to the formula above to obtain: $S_n=\dfrac{n}{2}[2a+(n-1)d] \\S_{30}=\dfrac{30}{2}[2(10) + (30-1)(-8)] \\S_{30}=15[20+29(-8)] \\S_{30}=15[20+(-232)] \\S_{30}=15(-212) \\S_{30}=-3180$
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