Think about Question 3 Given $x_{1}=1$, and $x_{n+1}=3 x_{n}^{2}+12 x_{n}+10$, find the general term formula of the sequence $\left\{x_{n}\right\}$.
Given: $x_{n+1}=3\left(x_{n}+2\right)^{2}-2$, which means $x_{n+1}+2=3\left(x_{n}+2\right)^{2}$, so $x_{n}+2=3\left(x_{n-1}+2\right)^{2}=3\left[3\left(x_{n-2}+2\right)^{2}\right]^{2}$
$$
\begin{array}{l}
=\cdots=3^{1+2+2^{2}+\cdots+2^{n-2}}\left(x_{1}+2\right) 2^{n-2} \\
=3^{2^{n-1}},
\end{array}
$$

which means $x_{n}=3^{2^{n}-1}-2$.