Answer
$343$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To evaluate the given summation expression, $
\displaystyle\sum_{i=1}^5 (3^i-4)
,$ substitute $
i
$ with the values from $
1
$ to $
5
$ and then simplify the expression.
$\bf{\text{Solution Details:}}$
Substituting $
i
$ with the numbers from $
1
$ to $
5
,$ the given expression evaluates to
\begin{array}{l}\require{cancel}
(3^1-4)+(3^2-4)+(3^3-4)+(3^4-4)+(3^5-4)
\\\\=
(3-4)+(9-4)+(27-4)+(81-4)+(243-4)
\\\\=
-1+5+23+77+239
\\\\=
343
.\end{array}
