9. Let the sequence $\left\{a_{n}\right\}$ have the sum of the first $n$ terms denoted by $S_{n}$. The sequence of these sums satisfies
$S_{n}+S_{n+1}+S_{n+2}=6 n^{2}+9 n+7(n \geq 1)$. Given that $a_{1}=1, a_{2}=5$, find the general term formula for the sequence $\left\{a_{n}\right\}$.
9. Analysis: $\left(S_{n+1}+S_{n+2}+S_{n+3}\right)-\left(S_{n}+S_{n+1}+S_{n+2}\right)=12 n+15(n \geq 1)$, is equivalent to $a_{n+1}+a_{n+2}+a_{n+3}=12 n+15(n \geq 1)$, and $\left(a_{n+1}+a_{n+2}+a_{n+3}\right)-\left(a_{n}+a_{n+1}+a_{n+2}\right)=12(n \geq 1)$, thus $a_{n+3}-a_{n}=12(n \geq 1)$, given $a_{1}=1, a_{2}=5, a_{3}=15-5-1=9$, we can conclude $a_{n}=4 n-3$