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
