Use $LaTeX: \displaystyle a_1=1$ and $LaTeX: \displaystyle a_2=9$ and $LaTeX: \displaystyle a_n=-4a_{n-1} +8a_{n-2}$ to find $LaTeX: \displaystyle a_{8}$

Finding the next term in the sequence gives $LaTeX: \displaystyle a_3=(-4)(1)+(8)(9)=68$
$LaTeX: \displaystyle a_{4}=(-4)(9)+(8)(68)=508$ .
$LaTeX: \displaystyle a_{5}=(-4)(68)+(8)(508)=3792$ .
$LaTeX: \displaystyle a_{6}=(-4)(508)+(8)(3792)=28304$ .
$LaTeX: \displaystyle a_{7}=(-4)(3792)+(8)(28304)=211264$ .
$LaTeX: \displaystyle a_{8}=(-4)(28304)+(8)(211264)=1576896$ .