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

Answer :

To find the number that follows the given Fibonacci numbers [tex]\( F(22) = 17,711 \)[/tex] and [tex]\( F(23) = 28,657 \)[/tex], we need to use the property of the Fibonacci sequence:

In a Fibonacci sequence, each number is the sum of the two preceding ones. Therefore, the pattern can be described as:

[tex]\[ F(n) = F(n-1) + F(n-2) \][/tex]

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

We want to find [tex]\( F(24) \)[/tex].

To do this, we calculate:

[tex]\[ F(24) = F(23) + F(22) \][/tex]
[tex]\[ F(24) = 28,657 + 17,711 \][/tex]

Now, let's add these numbers:
- [tex]\( 28,657 + 17,711 = 46,368 \)[/tex]

Thus, the number that follows is 46,368. Therefore, the correct choice is:

B. 46,368

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