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

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

anonymous · Answer

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

anonymous · Answer

@Mehek14

anonymous · Answer

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

anonymous · Answer

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'

anonymous · Answer

so it =1.618

anonymous · Answer

????? @oldrin.bataku

anonymous · Answer

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

anonymous · Answer

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