Question

Two large numbers of the Fibonacci sequence are F50 = 12,586,269,025 and F51 = 20,365,011,074.

What is the approximate value of the quotient ? f51/50

Answer 1

A. 1.618
B. 0.618
C. 2.618
D. 2
E. 3.142

Answer 2

@Mehek14

Answer 3

we have that \(F_n\approx\frac1{\sqrt5}\varphi^n\) for large \(n\) where \(\varphi=\frac12(1+\sqrt5)\approx1.618\)

Answer 4

so \(F_{n+1}/F_n\approx \varphi\approx 1.618\) for large \(n\); in this case, \(n=50\) is sufficiently big for this approximation to be 'good'

Answer 5

so it =1.618

Answer 6

????? @oldrin.bataku

Answer 7

check for yourself if you have a calculator; even just 3 digits of each are enough to give a decent approximation

Answer 8

\(F_{51}/F_{50}\approx 204/126=1.619\approx1.618\)