Question

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

Answer 1

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)=((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.