Solution of Inhomogeneous Recurrence Relation

If the average of two successive years' production is .5(a_{n}-a_{n-1}) = 2n+5 and a_{0}=3, find a_{n}.

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

Re: Solution of Inhomogeneous Recurrence Relation

Rewriting, you should get:

(1)

Replacing with you have:

(2)

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.