## College Algebra (11th Edition)

$S_3=18$
$\bf{\text{Solution Outline:}}$ To evaluate the given expression, $\displaystyle\sum_{i=1}^3 (i+4) ,$ 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+4 \\\\ a_1=5 .\end{array} Substituting $i$ with $3 ,$ then the last term, $a_n,$ is \begin{array}{l}\require{cancel} a_n=3+4 \\\\ a_n=7 .\end{array} With $i$ going from $1$ to $3 ,$ then there are a total of $3$ terms in the series. Hence, $n= 3 .$ 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_3=\dfrac{3}{2}(5+7) \\\\ S_3=\dfrac{3}{2}(12) \\\\ S_3=3(6) \\\\ S_3=18 .\end{array}