Answer
$S_7=-645$
Work Step by Step
We are asked to find the sum of:
$-15+30-60+\cdots-960$
This is a geometric sequence with $a_1=-15$. We find $r$:
$r=\frac{30}{-15}=-2$
We know that a geometric sequence has the form:
$a_{n}=ar^{n-1}$
We use this to find the number of terms:
$a_n=(-15)(-2)^{n-1}=-960$
$64=(-2)^{n-1}=\frac{(-2)^n}{-2}$
$-128=(-2)^n$
We see that $n$ must be odd:
$128=2^n$
$n=\log_2 128$
$n=7$
We know the partial sum of a geometric sequence is:
$S_n=a_1\frac{1-r^n}{1-r}$
Thus:
$S_{7}=-15 \frac{1-(-2)^{7}}{1-(-2)}=-645$
