Homework Help: Recurrsive Definitions

1. Nov 6, 2008

mamma_mia66

b]1. The problem statement, all variables and given/known data[/b]

Given a0=1 and a1=2, and

an=3an-1+an-2 for n>=2,

calculate a5 recursively

2. Relevant equations

3. The attempt at a solution

a5=3a4+a3
=3(3a3+a2)+a3=10a3+3a2
=10(3a2+a1)+3a2
=33a2+10a1
=33(3a1+a0)+10a1
=99a1+33a0+10a1
=109a1+33a0

Last edited: Nov 6, 2008
2. Nov 6, 2008

Dick

Right. But isn't it easier to start with a0=1 and a1=2 and work your way up to a5? That way it's just arithmetic, not algebra.

3. Nov 6, 2008

vvvidenov

Thank you for the proof of my work. That is the way the professor wants us to do it.

4. Nov 7, 2008

HallsofIvy

Doesn't your professor want you to complete the problem?

You were told that a0= 1 and a1= 2. The complete answer is NOT "109a1+33a0", it is 109(1)+ 33(2)= 109+ 66= 175.

I suspect you have misunderstood what your professor wants.

5. Nov 7, 2008

mamma_mia66

I completed. It most important for me that I did it right.