Question

If $f(x + 2) = f(x) + f(x + 1)$ for all positive integers $x$, and $f(11) = 91$, $f(15) = 617$, then $f(10)$ equals.

Accepted Answer

54. Let $f(10) = a$ and $f(11) = 91$. $f(12) = f(10) + f(11) = a + 91$ $f(13) = f(11) + f(12) = 91 + a + 91 = a + 182$ $f(14) = f(12) + f(13) = a + 91 + a + 182 = 2a + 273$ $f(15) = f(13) + f(14) = a + 182 + 2a + 273 = 3a + 455$ Given $f(15) = 617$: $3a + 455 = 617 \Rightarrow 3a = 162 \Rightarrow a = 54$.

Recursive Function Value

Explanation

Practise this under exam conditions