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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.

2 Answers 2