\begin{align*}
a_1 \amp = 3a_0 + 2\\
a_2 \amp = 3(a_1) + 2 = 3(3a_0 + 2) + 2\\
a_3 \amp = 3[a_2] + 2 = 3[3(3a_0 + 2) + 2] + 2\\
\vdots \amp \qquad \vdots \qquad \qquad \vdots\\
a_n \amp = 3(a_{n-1}) + 2 = 3(3(3(3\cdots(3a_0 + 2) + 2) + 2)\cdots + 2)+ 2
\end{align*}
in-context