Answer
$a_n=3\left(-2\right)^{n-1}$
Work Step by Step
$a_4=-24$ and $a_{11}=3072$
$\frac{a_{11}}{a_4}=\frac{ar^{10}}{ar^3}=\frac{3072}{-24}=-128=r^7$
$\implies r=\left(-128\right)^{\frac{1}{7}}=-2.$
$a_4=ar^3=a\left(-2\right)^3=a\left(-8\right)=-24$
$\implies a=3$
The $n^{th}$ term is therefore
$a_n=3\left(-2\right)^{n-1}$