Question

Find f(5) for this sequence:

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

f(5) = ______

Answer 1

http://m.wolframalpha.com/input/?i=f(n)%3Df(n-1)%2Bf(n-2)%2C+f(1)%3D1%2C+f(2)%3D2

Answer 2

one approach (the long way)
5>2
f(5) = f(1) + f(2) + f(5 - 1)
f(4) = (f1) + f(2) + f(4 - 1)
f(3) = f(1) + f(2) + f(3-1)
f(5)= f(1) +f(2) + f(1) + f(2) + f(1) + f(2) + f(2)
f(5) = 3*f(1) + 3f(2) = 3*(2 + 5) = 21

Answer 3

correction I missed an (f2) should be 3*f(1) + 4*f(2)
so it would be 21 + 5 = 26