Problem
Two large numbers of the Fibonacci sequence are $F(50)=12,586,269,025$ and $F(51)=20,365,011,074$. If these two numbers are added together, what number results? A. $F(52)$ B. $F(101)$ C. $F(53)$ D. $F(49)$
Solution
Step 1 ：The Fibonacci sequence is defined as \(F(n) = F(n-1) + F(n-2)\) for \(n > 1\), and \(F(0) = 0\), \(F(1) = 1\).
Step 2 ：Two large numbers of the Fibonacci sequence are \(F(50)=12,586,269,025\) and \(F(51)=20,365,011,074\).
Step 3 ：If these two numbers are added together, we should get \(F(52)\) according to the definition of the Fibonacci sequence.
Step 4 ：So, \(F(50) + F(51) = F(52)\).
Step 5 ：Final Answer: The sum of \(F(50)\) and \(F(51)\) is \(F(52)\), so the correct answer is \(\boxed{A}\).
