Given that $m_1= 2$ and $m_2 = 9$ and that $m_n = 2m_{n-1} + 3m_{n-2}$ for $n \geq 3$
This is what I've done so far.
$3^{n+1}$ = $3^n \cdot 3$
$3^{n+1} \geq 3 \cdot (2m_{n-1} + 3m_{n-2})$
$3^{n+1} \geq 6m_{n-1} + 9m_{n-2}$
$m_{n+1} = 7m_{n-1} + 6m_{n-2}$
Prove by induction.