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Given the two Fibonacci numbers below, which number would follow?

[tex]\[ F(22) = 17,711 \][/tex] and [tex]\[ F(23) = 28,657 \][/tex]

A. 1.618
B. 0.618
C. 10,946
D. 46,368

Answer :

To find the number that follows the given Fibonacci numbers, we need to understand how Fibonacci numbers are generated. In the Fibonacci sequence, each number is the sum of the two preceding ones.

We are given two Fibonacci numbers:
- [tex]\( F(22) = 17,711 \)[/tex]
- [tex]\( F(23) = 28,657 \)[/tex]

To find the next Fibonacci number, [tex]\( F(24) \)[/tex], we add the given numbers:

1. Start with the two known Fibonacci numbers:
- [tex]\( F(22) = 17,711 \)[/tex]
- [tex]\( F(23) = 28,657 \)[/tex]

2. Add these numbers together to find the next number:
[tex]\[
F(24) = F(22) + F(23) = 17,711 + 28,657
\][/tex]

3. Calculate the sum:
- [tex]\( 17,711 + 28,657 = 46,368 \)[/tex]

Therefore, the number that follows is [tex]\( 46,368 \)[/tex]. So the answer is:

D. 46,368

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