Answer
$135$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To evaluate the given summation expression, $
\displaystyle\sum_{i=3}^7 (5i+2)
,$ substitute $
i
$ with the values from $
3
$ to $
7
$ and then simplify the expression.
$\bf{\text{Solution Details:}}$
Substituting $
i
$ with the numbers from $
3
$ to $
7
,$ the given expression evaluates to
\begin{array}{l}\require{cancel}
(5(3)+2)+(5(4)+2)+(5(5)+2)+(5(6)+2)+(5(7)+2)
\\\\=
(15+2)+(20+2)+(25+2)+(30+2)+(35+2)
\\\\=
17+22+27+32+37
\\\\=
135
.\end{array}
