Given a sequence of #'s $\displaystyle a_1, a_2, a_3, a_4, \ldots$ which is defined by:

$\displaystyle a_1 = 1$

$\displaystyle a_2 = 2$

$\displaystyle a_n = a_{n-1} + a_{n-2}\ \ n \geq 3$

Prove, using math induction:

$\displaystyle a_n < \left(\frac{7}{4}\right)^{n} \ \forall$ integers $\displaystyle n \geq 1$