Chapter 8, Sequences and Series - Section 8.3 - Geometric Sequences - 8.3 Exercises - Page 615: 61

$S_6=-105$

We need to find: $\sum_{k=1}^{6}5(-2)^{k-1}$ We see that this is a geometric sequence with $a=5$ and $r=-2$. We know the partial sum of a geometric sequence is: $S_n=a_1\frac{1-r^n}{1-r}$ $S_6=5\frac{1-(-2)^{6}}{1-(-2)}=-105$