Recursive Definition of a Sequence: Solving for a5

[mamma_mia66]

b]1. Homework Statement [/b]

Given a₀=1 and a₁=2, and

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

calculate a₅ recursively

Homework Equations

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

 

[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.

 

[vvvidenov]

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

 

[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.

 

[mamma_mia66]

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