Answer
$a_n=625\left(\frac{1}{5}\right)^{n-1}$
Work Step by Step
$625, 125, 25, 5, 1, 0.2, . . .$
$\frac{a_2}{a_1}=\frac{125}{625}=\frac{1}{5}=r$
$ra_2=\frac{1}{5}\times125=25=a_3$
$ra_3=\frac{1}{5}\times25=5=a_4$
and so on. The sequence is geometric with ratio $r=\frac{1}{5}$. The $n^{th}$ term is given by
$a_n=625\left(\frac{1}{5}\right)^{n-1}$