Thread: Recursively defined functions

Can someone help me get started with this...

Find f(1), f(2), f(3), f(4), and f(5) if f(n) is defined recursively by f(0)=3 and for n=0,1,2,...
f(n+1)=-2f(n)

I'm not looking for the answer, but for help in understanding.

Hello

Originally Posted by sjenkins

Find f(1), f(2), f(3), f(4), and f(5) if f(n) is defined recursively by f(0)=3 and for n=0,1,2,...
f(n+1)=-2f(n)

I'm not looking for the answer, but for help in understanding.

We're given . To find choose such that . This gives . Then use the relation with : . Does it help ?

I still feel so confused, but maybe if I give an example that is given in the book, I will understand what is going on.

Suppose that f is defined recursively by
f(0)=3
f(n+1)=2f(n)+3
Find f(1), f(2), f(3), f(4)

Solution:
f(1)=2f(0)+3=2X3+3=9
f(2)=2f(1)+3=2X9+3=21

Where does that 9 come from????

Originally Posted by sjenkins

Solution:
f(1)=2f(0)+3=2X3+3=9
f(2)=2f(1)+3=2X9+3=21

Where does that 9 come from????

That's the value of . is given by and has has been computed just before, we know that it equals 9.

Ohhhhh....that makes complete sense. I knew I was just missing something simple.

Thanks again for the help!!