200 Followers Problem

Algebra Level 5

If \(f(x)\) is a 5th degree monic polynomial such that :

\(f(1) = 1\)

\(f(2) = 2\)

\(f(3) = 5\)

\(f(4) = 13\)

\(f(5) = 34\)

then find the value of \((f(6) + f(7) + f(8))\)

This problem is original

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