Question 99
A sequence $(a_n)$ is defined by
$$
a_1 = 1, \quad a_n = 3a_{n-1} + 2^{n-1}, \quad \text{for } n \ge 2.
$$
Find a formula for the general term $a_n$ in terms of $n$.
$$
a_1 = 1, \quad a_n = 3a_{n-1} + 2^{n-1}, \quad \text{for } n \ge 2.
$$
Find a formula for the general term $a_n$ in terms of $n$.