Use $LaTeX: \displaystyle a_1=2$ and $LaTeX: \displaystyle a_2=5$ and $LaTeX: \displaystyle a_n=-9a_{n-1} +9a_{n-2}$ to find $LaTeX: \displaystyle a_{8}$

Finding the next term in the sequence gives $LaTeX: \displaystyle a_3=(-9)(2)+(9)(5)=27$
$LaTeX: \displaystyle a_{4}=(-9)(5)+(9)(27)=198$ .
$LaTeX: \displaystyle a_{5}=(-9)(27)+(9)(198)=1539$ .
$LaTeX: \displaystyle a_{6}=(-9)(198)+(9)(1539)=12069$ .
$LaTeX: \displaystyle a_{7}=(-9)(1539)+(9)(12069)=94770$ .
$LaTeX: \displaystyle a_{8}=(-9)(12069)+(9)(94770)=744309$ .