Answer to Question #241814 in Math for Ers

Question

The 80th term of fibonacii sequence is?

Answer 1

Use Binet formula

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

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

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

$$F_{80}=\dfrac{(1+\sqrt{5})^{80}-(1-\sqrt{5})^{80}}{2^{80}\sqrt{5}}$$

$$F_{80}= 14472334024676221$$