184. The sequence $\left(a_{n}\right)$ satisfies the conditions:

$$
a_{1}=3, \quad a_{2}=9, \quad a_{n+1}=4 a_{n}-3 a_{n-1}(n>1)
$$

Find the formula for the general term of the sequence.
$\triangle$ Let's compute the first few terms of the sequence, starting from $a_{3}$:

$a_{3}=4 a_{2}-3 a_{1}=4 \cdot 9-3 \cdot 3=27=3^{3}$,

$a_{4}=4 a_{3}-3 a_{2}=4 \cdot 27-3 \cdot 9=81=3^{4}$

$a_{5}=4 a_{4}-3 a_{3}=4 \cdot 81-3 \cdot 27=243=3^{5}$.

It seems that for any natural number $n$, $a_{n}=3^{n}$. Prove this formula independently using mathematical induction.

Answer: $a_{n}=3^{n}$.