Use the value of phi = 1.618 to predict the 23rd number in the Fibonacci sequence. The 22nd number in the sequence is 17,711. - 10,946 - 17,711 - 22,897 - 28,656

Question

asked Feb 20, 2022 217k views

1 Answer

Jack Hales · Answer 1 · 2022-02-24T08:13:27+0000

Given:

$\phi=1.618$

22nd number in Fibonacci sequence = 17,711

To find:

The 23rd number in the Fibonacci sequence.

Solution:

The nth term of a Fibonacci sequence is:

$f_n=(\phi^n-(1-\phi)^n)/(√(5))$

Substituting
$\phi=1.618, n=21$ , we get

f_(21)=((1.618)^(21)-(1-1.618)^(21))/(√(5))

f_(21)=10941.1724024

$f_(21)\approx 10941$

Now,

f_(23)=f_(21)+f_(22)

f_(23)=10941+17711

f_(23)=28652

It is about 28,656. Therefore, the correct option is D.