Answer
$S_{15}=870$
Work Step by Step
RECALL:
The sum of the first $n$ terms ($S_n$) of an arithmetic sequence is given by the formula:
$S_n=\dfrac{n}{2}\left[2a+(n-1)d\right]$
where
$a$ = first term
$d$ = common difference
The given arithmetic sequence has:
$a=-40
\\d=14$
Thus, to find the sum of the first 15 terms, substitute the given values to the formula above to obtain:
$S_n=\dfrac{n}{2}[2a+(n-1)d]
\\S_{15}=\dfrac{15}{2}[2(-40) + (15-1)(14)]
\\S_{15}=\dfrac{15}{2}[-80+14(14)]
\\S_{15}=\dfrac{15}{2}(-80+196)
\\S_{15}=\dfrac{15}{2}(116)
\\S_{15}=870$
