Given an inductive function, how to calculate?

Question

Currently having slight difficulty figuring out how to solve this.

Given is;

$$\begin{align}f(0) &= -3\\ f(1)&= 2 \\ f(n) &= f( n - 2 ) + 2 f( n - 1)\end{align}$$

Now, I need to calculate $f(5)$.

I'm not sure how to handle a function like this. Fill the N's and dissasemble?

score 2 · Accepted Answer · answered Sep 24 '13 at 14:18

2

To calculate $f(5)$ you can just start using the recursion: \begin{align*} f(2) &= f(0) + 2f(1)\\ &= -3 + 4\\ &= 1\\ f(3) &= f(1) + 2f(2)\\ &= 2 + 2 \\ &= 4\\ f(4) &= f(2) + 2f(3)\\ &= 1 + 8\\ &= 9\\ f(5) &= f(3) + 2f(4)\\ &= 4 + 18\\ &= 22. \end{align*}

answered Sep 24 '13 at 14:18

martini

84,101

Thanks a lot! Would it be reliable to just grab f(0) and f(1), getting the difference from that step and just apply that for 5 steps? – MichaelP Sep 24 '13 at 14:26
What difference? – martini Sep 24 '13 at 14:26
f(0) = -3, f(1) = 2 , difference being 5, then just count up. F(2) = 7, etc. – MichaelP Sep 24 '13 at 14:29
But $f(2) - f(1) \ne f(1) - f(0)$. – martini Sep 24 '13 at 14:30
Ah, yes, i see what you did there. Not really understanding yet why you'd start with f(2) – MichaelP Sep 24 '13 at 14:31
As I can compute $f(2)$ from the given values. – martini Sep 24 '13 at 14:32
Doh! Ofcourse! Thanks alot again! – MichaelP Sep 24 '13 at 14:33

Given an inductive function, how to calculate?

1 Answers1