$a_n = \frac{1}{\sqrt{5}} ((\frac{1+\sqrt{5}}{2})^{n+1} - (\frac{1-\sqrt{5}}{2})^{n+1})$

$a_n = (\frac{1+\sqrt{5}}{2})^n$

$a_n = \frac{1}{\sqrt{5}} ((\frac{1+\sqrt{5}}{2})^n + (\frac{1-\sqrt{5}}{2})^n)$

$a_n = 2^n$