Question

Find f(5)
f(1) = 2 and f(2) = 5, f(n) = f(1) + f(2) + f(n - 1), for n > 2.

f(5) = ______

Answer 1

All right, we need f(3) and f(4) to solve this question.

Given f(1)=2 and f(2)=3, we have f(3) = f(1)+ f(2)+f(2), which in turn is 2+3+3 = 8, so f(3)=8
f(4) is f(1)+f(2)+f(3), so we have 2+3+8= 13.
We have found f(4), which is necessary to find f(5).
f(5) = f(1)+f(2)+f(4) = 2+3+13=18.