Answer
$a_n=2(5)^{n-1}$
Work Step by Step
$a_4=250$ and $a_9=781250$
$\frac{a_9}{a_4}=\frac{ar^8}{ar^3}=\frac{781250}{250}=3125=r^5$
$\implies r=(3125)^{\frac{1}{5}}=5.$
$a_4=ar^3=a(5^3)=125a=250$
$\implies a=2$
The $n^{th}$ term is therefore
$a_n=2(5)^{n-1}$