College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 7 - Section 7.2 - Arithmetic Sequences and Series - 7.2 Exercises: 54

Answer

$S_5=-25$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To evaluate the given expression, $ \displaystyle\sum_{i=1}^5 (i-8) ,$ use the formula for finding the sum of $n$ terms that form an arithmetic sequence. $\bf{\text{Solution Details:}}$ Substituting $i$ with $ 1 ,$ then the first term, $a_1,$ is \begin{array}{l}\require{cancel} a_1=1-8 \\\\ a_1=-7 .\end{array} Substituting $i$ with $ 5 ,$ then the last term, $a_n,$ is \begin{array}{l}\require{cancel} a_n=5-8 \\\\ a_n=-3 .\end{array} With $i$ going from $ 1 $ to $ 5 ,$ then there are a total of $ 5 $ terms in the series. Hence, $n= 5 .$ Using the formula for finding the sum of $n$ terms that form an arithmetic sequence, which is given by $S_n=\dfrac{n}{2}(a_1+a_n),$ then \begin{array}{l}\require{cancel} S_5=\dfrac{5}{2}(-7+(-3)) \\\\ S_5=\dfrac{5}{2}(-7-3) \\\\ S_5=\dfrac{5}{2}(-10) \\\\ S_5=5(-5) \\\\ S_5=-25 .\end{array}
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