Fibonacci Function

Algebra Level 5

Let f(x)f(x) be a quintic polynomial such that

f(1)=1f(2)=1f(3)=2f(4)=3f(5)=5f(6)=8. \begin{array} { r l } f(1) & = 1 \\ f(2) & = 1 \\ f(3) & = 2 \\ f(4) & = 3 \\ f(5) & = 5 \\ f(6) & = 8. \\ \end{array}

Determine f(7) f(7).


Note: Many people are answering this incorrectly because they think it is the Fibonacci sequence, but this problem is asking about a quintic polynomial that passes through those points. That does not necessarily mean the next term behaves as the Fibonacci sequence would.

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