Answer
$a_n=-160(-\frac{1}{2})^n$
Work Step by Step
$a_1=5$
$r=\frac{a_2}{a_1}=\frac{a_3}{a_2}$
$r=\frac{-40}{80}=\frac{20}{-40}=-\frac{1}{2}$
$a_n=a_1r^{n-1}$
$a_n=80(-\frac{1}{2})^{n-1}=80(-\frac{1}{2})^n(-\frac{1}{2})^{-1}=80(-\frac{1}{2})^n(-2)=-160(-\frac{1}{2})^n$
