Answer
$a_n=8\left(-3\right)^{n-1}$
Work Step by Step
$a_6=-1944$ and $a_{9}=52488$
$\frac{a_{9}}{a_6}=\frac{ar^{8}}{ar^5}=\frac{52488}{-1944}=-27=r^3$
$\implies r=\left(-27\right)^{\frac{1}{3}}=-3.$
$a_6=ar^5=a\left(-3\right)^5=a\left(-243\right)=-1944=8$
$\implies a=8$
The $n^{th}$ term is therefore
$a_n=8\left(-3\right)^{n-1}$