To solve this problem, we need to add the two given Fibonacci numbers and determine what the result represents within the Fibonacci sequence.
We are given:
[tex]\[ F(51) = 20,365,011,074 \][/tex]
[tex]\[ F(52) = 32,951,280,099 \][/tex]
Step-by-step solution:
1. First, recall the definition of the Fibonacci sequence, where each number in the sequence is the sum of the two preceding numbers. That is:
[tex]\[ F(n) = F(n-1) + F(n-2) \][/tex]
2. Using the definition of the Fibonacci sequence, if we know [tex]\( F(51) \)[/tex] and [tex]\( F(52) \)[/tex], we can find [tex]\( F(53) \)[/tex] by adding these two numbers together:
[tex]\[ F(53) = F(52) + F(51) \][/tex]
3. Substitute the given values into the equation:
[tex]\[ F(53) = 32,951,280,099 + 20,365,011,074 \][/tex]
4. Perform the addition:
[tex]\[ 32,951,280,099 + 20,365,011,074 = 53,316,291,173 \][/tex]
5. The result of this addition is [tex]\( 53,316,291,173 \)[/tex].
Given this result and the context of the Fibonacci sequence, we can see that the resultant number matches the description of [tex]\( F(53) \)[/tex].
Therefore, the correct answer is:
B. [tex]\( F(53) \)[/tex]
