Answer
a. $a_n=-5(-2)^{n-1}$
b. $640$
c. $1705$
Work Step by Step
a. Based on the given sequence, we have
$a_1=-5, r=\frac{10}{-5}=-2$
hus
$a_n=a_1(r)^{n-1}=-5(-2)^{n-1}$
b. For $n=8$, we have
$a_8=-5(-2)^{8-1}=640$
c. For $n=10$, the sum is
$S_n=\frac{a_1(1-r^n)}{1-r}$
Thus
$S_{10}=\frac{-5(1-(-2)^{10})}{1-(-2)}=1705$
