Use $LaTeX: \displaystyle a_1=5$ and $LaTeX: \displaystyle a_2=-8$ and $LaTeX: \displaystyle a_n=3a_{n-1} +7a_{n-2}$ to find $LaTeX: \displaystyle a_{6}$

Finding the next term in the sequence gives $LaTeX: \displaystyle a_3=(3)(5)+(7)(-8)=-41$
$LaTeX: \displaystyle a_{4}=(3)(-8)+(7)(-41)=-311$ .
$LaTeX: \displaystyle a_{5}=(3)(-41)+(7)(-311)=-2300$ .
$LaTeX: \displaystyle a_{6}=(3)(-311)+(7)(-2300)=-17033$ .