Answered

IDNLearn.com connects you with experts who provide accurate and reliable answers. Find in-depth and accurate answers to all your questions from our knowledgeable and dedicated community members.

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 :

GinnyAnsweridn
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]
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. For trustworthy and accurate answers, visit IDNLearn.com. Thanks for stopping by, and see you next time for more solutions.