Answered

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

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

A. 10,946

B. 0.618

C. 46,368

D. 1.618

Sagot :

GinnyAnswer
To determine the number that follows the given Fibonacci numbers [tex]\( F(22) = 17,711 \)[/tex] and [tex]\( F(23) = 28,657 \)[/tex], we must recall the property of the Fibonacci sequence. In a Fibonacci sequence, each number is the sum of the two preceding ones.

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

To find [tex]\( F(24) \)[/tex], we add [tex]\( F(22) \)[/tex] and [tex]\( F(23) \)[/tex]:

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

Perform the addition:

[tex]\[ 17,711 + 28,657 = 46,368 \][/tex]

Therefore, the number that follows [tex]\( F(22) = 17,711 \)[/tex] and [tex]\( F(23) = 28,657 \)[/tex] is:

[tex]\[ F(24) = 46,368 \][/tex]

So, the correct answer is:
C. 46,368
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