Question

What is the 99th term of fibonacci sequence?

Answer 1

Use Binet formula

$$F_n=\dfrac{\alpha^n-\beta^n}{\alpha-\beta}$$

$$\alpha=\dfrac{1+\sqrt{5}}{2}, \beta=\dfrac{1-\sqrt{5}}{2}$$

$$\alpha-\beta=\sqrt{5}$$

$$F_{99}=\dfrac{(1+\sqrt{5})^{99}-(1-\sqrt{5})^{99}}{2^{99}\sqrt{5}}$$

$$F_{99}= 218922995834555169026$$