Use $LaTeX: \displaystyle a_1=3$ and $LaTeX: \displaystyle a_2=4$ and $LaTeX: \displaystyle a_n=8a_{n-1} +1a_{n-2}$ to find $LaTeX: \displaystyle a_{7}$

Finding the next term in the sequence gives $LaTeX: \displaystyle a_3=(8)(3)+(1)(4)=28$
$LaTeX: \displaystyle a_{4}=(8)(4)+(1)(28)=60$ .
$LaTeX: \displaystyle a_{5}=(8)(28)+(1)(60)=284$ .
$LaTeX: \displaystyle a_{6}=(8)(60)+(1)(284)=764$ .
$LaTeX: \displaystyle a_{7}=(8)(284)+(1)(764)=3036$ .