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Two large numbers of the Fibonacci sequence are [tex]$F(51)=20,365,011,074$[/tex] and [tex]$F(52)=32,951,280,099$[/tex]. If these two numbers are added together, what number results?

A. [tex][tex]$F(52)$[/tex][/tex]

B. [tex]$F(50)$[/tex]

C. [tex]$F(103)$[/tex]

D. [tex][tex]$F(53)$[/tex][/tex]

Sagot :

GinnyAnswer
To solve this problem, we need to understand some basics about the Fibonacci sequence. The Fibonacci sequence is defined such that each subsequent number is the sum of the two preceding ones. Mathematically, it is expressed as:

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

Given the sequence and the provided values:
[tex]\[ F(51) = 20,365,011,074 \][/tex]
[tex]\[ F(52) = 32,951,280,099 \][/tex]

We are asked to find the sum of these two numbers:
[tex]\[ F(51) + F(52) \][/tex]

According to the Fibonacci sequence's properties, adding [tex]\( F(51) \)[/tex] and [tex]\( F(52) \)[/tex] will give us the next number in the sequence, which is [tex]\( F(53) \)[/tex]:

[tex]\[ F(53) = F(51) + F(52) \][/tex]

Now, substituting the given values:
[tex]\[ F(53) = 20,365,011,074 + 32,951,280,099 \][/tex]

Performing the addition:
[tex]\[ 20,365,011,074 + 32,951,280,099 = 53,316,291,173 \][/tex]

Therefore, the number resulting from adding [tex]\( F(51) \)[/tex] and [tex]\( F(52) \)[/tex] is:

[tex]\[ F(53) = 53,316,291,173 \][/tex]

So, the correct answer is:
D. [tex]\( F(53) \)[/tex]
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