# Math Help - Solution of Inhomogeneous Recurrence Relation

1. ## Solution of Inhomogeneous Recurrence Relation

If the average of two successive years' production is .5(an-an-1) = 2n+5 and a0=3, find an.

I rewrote this as an=-an-1 + 4n +10, is that right? I need to find a general solution to the homogeneous solution and use the initial condition to find an, which is the solution to the inhomogeneous recurrence relation. Any help please?

2. ## Re: Solution of Inhomogeneous Recurrence Relation

Rewriting, you should get:

(1) $a_{n}=a_{n-1}+4n+10$

Replacing $n$ with $n+1$ you have:

(2) $a_{n+1}=a_{n}+4(n+1)+10$

Now, subtract (1) from (2) to get another recurrence, then repeat the above process to get a homogeneous recurrence. From the characteristic roots, you then can obtain the general solution, and then use your initial values to determine the parameters.