Use $LaTeX: \displaystyle a_1=3$ and $LaTeX: \displaystyle a_2=6$ and $LaTeX: \displaystyle a_n=2a_{n-1} -2a_{n-2}$ to find $LaTeX: \displaystyle a_{8}$

Finding the next term in the sequence gives $LaTeX: \displaystyle a_3=(2)(3)+(-2)(6)=-6$
$LaTeX: \displaystyle a_{4}=(2)(6)+(-2)(-6)=24$ .
$LaTeX: \displaystyle a_{5}=(2)(-6)+(-2)(24)=-60$ .
$LaTeX: \displaystyle a_{6}=(2)(24)+(-2)(-60)=168$ .
$LaTeX: \displaystyle a_{7}=(2)(-60)+(-2)(168)=-456$ .
$LaTeX: \displaystyle a_{8}=(2)(168)+(-2)(-456)=1248$ .