It's a geometric sequence.
[tex]4,-12,36,... \\ \\
a_1=4 \\
r=\frac{a_2}{a_1}=\frac{-12}{4}=-3 \\ \\
a_n=a_1 \times r^{n-1} \\
a_n=4 \times (-3)^{n-1} \\
a_n=4 \times (-3)^{-1} \times (-3)^n \\
a_n=4 \times (-\frac{1}{3}) \times (-3)^n \\
a_n=-\frac{4}{3}(-3)^n[/tex]
It's the sum for term 4 through term 15.
[tex]\boxed{ \sum\limits_{n=4}^{15} (\frac{4}{3}(-3)^n)}[/tex]
