$\lim_{n\to\infty} \frac{F_n}{F_{n-1}} = \phi = \frac{1+\sqrt{5}}{2}$

$F_n = \frac{\phi^n - \psi^n}{\sqrt{5}}$ where $\psi = \frac{1-\sqrt{5}}{2}$

For large $n$, $F_n \approx \phi^n / \sqrt{5}$

All of the above