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

Finding the next term in the sequence gives $LaTeX: \displaystyle a_3=(-1)(-1)+(-2)(-2)=5$
$LaTeX: \displaystyle a_{4}=(-1)(-2)+(-2)(5)=-8$ .
$LaTeX: \displaystyle a_{5}=(-1)(5)+(-2)(-8)=11$ .