Question

Find f(5) for this sequence:

f(1) = 2 and f(2) = 3, f(n) = f(1) + f(2) + f(n - 1), for n > 2.

f(5) = ______

Answer 1

@jim_thompson5910 @Hero @mathstudent55 help please?

Answer 2

Start with f(3) and work our way up

Answer 3

F(3) would be 4? Or is it saying to substitute n with 5? I'm completely lost on how to do this.

Answer 4

Since f(1) = 2 and f(2) = 3, substitute those in to the given equation

f(n) = f(1) + f(2) + f(n - 1) to get
f(n) = 2 + 3 + f(n - 1) which simplifies to
f(n) = 5 + f(n - 1)

So far

f(3) = 5 + f(3 - 1)
f(3) = 5 + f(2)
f(3) = 5 + 3
f(3) = 8

Answer 5

So 4 would be 13?