請教一題遞迴關係式的題目

\((a_{n+2}+k)=(a_{n+1}+k)+2(a_n+k)\)
\(a_{n+2}=a_{n+1}+2a_n+2k\)，\(\displaystyle k=\frac{3}{2}\)
\(\displaystyle (a_{n+2}+\frac{3}{2})=(a_{n+1}+\frac{3}{2})+2(a_n+\frac{3}{2})\)
令\(\displaystyle b_n=a_n+\frac{3}{2}\)
\(b_{n+2}=b_{n+1}+2b_n\)