Answer
(a)
$r=\frac{1}{5}$
(b)
$S_8=\frac{5^8-1}{4·5^5}=31.24992$
Work Step by Step
$a=25$ and $a_4=\frac{1}{5}$
(a)
$a_n=ar^{n-1}$
$a_5=ar^{4-1}$
$\frac{1}{5}=25r^3$
$r^3=\frac{1}{125}$
$r=\frac{1}{5}$
(b)
$S_n=a\frac{1-r^n}{1-r}$
$S_8=25\frac{1-(\frac{1}{5})^8}{1-\frac{1}{5}}=\frac{25-(\frac{1}{5})^6}{\frac{4}{5}}\frac{5^6}{5^6}=\frac{5^8-1}{4·5^5}=31.24992$
