Answer
$875$
Work Step by Step
Using $
S_n=\dfrac{n}{2}(2a_1+(n-1)d)
$ or the formula for the sum of $n$ terms that form an arithmetic sequence, with $a_1=-1$, $d=3,$ and $n=25,$ then
\begin{align*}\require{cancel}
S_n&=\dfrac{25}{2}(2(-1)+(25-1)3)
\\\\&=
\dfrac{25}{2}(2(-1)+(24)3)
\\\\&=
\dfrac{25}{2}(-2+72)
\\\\&=
\dfrac{25}{2}(70)
\\\\&=
\dfrac{25}{\cancelto{1}2}(\cancelto{35}{70})
&(\text{cancel common factor equal to }2)
\\\\&=
875
.\end{align*}
Hence, the sum of the first $25$ terms, $-1+2+5+...$, is $875$.
