Answer
$a_n=16384\left(\frac{1}{4}\right)^{n-1}$
Work Step by Step
$a_4=256$ and $a_{10}=\frac{1}{16}$
$\frac{a_{10}}{a_4}=\frac{ar^{10}}{ar^4}=\frac{\frac{1}{16}}{256}=\frac{1}{4096}=r^6$
$\implies r=(\frac{1}{4096})^{\frac{1}{6}}=\frac{1}{4}.$
$a_4=ar^3=a\left(\frac{1}{4}\right)^3=a\left(\frac{1}{64}\right)=256$
$\implies a=16384$
The $n^{th}$ term is therefore
$a_n=16384\left(\frac{1}{4}\right)^{n-1}$