Answer
$S_{25}=6850$
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:
$a=-2
\\d=23$
Thus, to find the sum of the first 25 terms, substitute the given values to the formula above to obtain:
$S_n=\dfrac{n}{2}[2a+(n-1)d]
\\S_{25}=\dfrac{25}{2}[2(-2) + (25-1)(23)]
\\S_{25}=\dfrac{25}{2}[-4+24(23)]
\\S_{25}=\dfrac{25}{2}(-4+552)
\\S_{25}=\dfrac{25}{2}(548)
\\S_{25}=6850$