-3+6-12+24 <---- notice the terms firstly, they go as
-3 , +6 , -12 , +24 ,.... <---- to get the next term's value, you multiply it by -2
thus, is a geometric sequence, and -2 is the "common difference", and the first term is -3 of course.
so... what's the sum of the first 7 terms?
[tex]\bf \qquad \qquad \textit{sum of a finite geometric sequence}\\\\
S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
a_1=-3\\
r=-2\\
n=7
\end{cases}[/tex]
[tex]\bf S_7=\sum\limits_{i=1}^{7}\ -3\cdot (-2)^{i-1}\implies
S_7=-3\left( \cfrac{1-(-2)^7}{1-(-2)} \right)
\\\\\\
S_7=-3\left( \cfrac{1-(-128)}{1+2}\right)\implies S_7=-3\left( \cfrac{129}{3} \right)\implies S_7=-3(43)
\\\\\\
S_7=-129[/tex]
