Answer to Question #241814 in Math for Ers

Question #241814
The 80th term of fibonacii sequence is?
1
Expert's answer
2021-09-28T12:58:17-0400

Use Binet formula


Fn=αnβnαβF_n=\dfrac{\alpha^n-\beta^n}{\alpha-\beta}

α=1+52,β=152\alpha=\dfrac{1+\sqrt{5}}{2}, \beta=\dfrac{1-\sqrt{5}}{2}

αβ=5\alpha-\beta=\sqrt{5}

F80=(1+5)80(15)802805F_{80}=\dfrac{(1+\sqrt{5})^{80}-(1-\sqrt{5})^{80}}{2^{80}\sqrt{5}}

F80=14472334024676221F_{80}= 14472334024676221


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