Answer
$-4$
Work Step by Step
Using the given general term, $
a_n=(n-3)(n+2)
,$ then,
\begin{array}{l}
a_1=(1-3)(1+2)\\
a_1=(-2)(3)\\
a_1=-6
,\\\\
a_2=(2-3)(2+2)\\
a_2=(-1)(4)\\
a_2=-4
,\\\\
a_3=(3-3)(3+2)\\
a_3=(0)(5)\\
a_3=0
,\\\\
a_4=(4-3)(4+2)\\
a_4=(1)(6)\\
a_4=6
\end{array}
Hence, $
S_4=-6+(-4)+0+6
=
-4
.$
