Answer
$51$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To evaluate the given summation expression, $
\displaystyle\sum_{i=1}^6 (3i-2)
,$ substitute $i$ with the values from $
1
$ to $
6
$ and then simplify the expression.
$\bf{\text{Solution Details:}}$
Substituting $i$ with the numbers from $
1
$ to $
6
,$ the given expression evaluates to
\begin{array}{l}\require{cancel}
(3(1)-2)+(3(2)-2)+(3(3)-2)+(3(4)-2)+(3(5)-2)+(3(6)-2)
\\\\=
(3-2)+(6-2)+(9-2)+(12-2)+(15-2)+(18-2)
\\\\=
1+4+7+10+13+16
\\\\=
51
.\end{array}
