## College Algebra (11th Edition)

Published by Pearson

# Chapter 7 - Section 7.2 - Arithmetic Sequences and Series - 7.2 Exercises - Page 646: 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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