Thread: Solution of Inhomogeneous Recurrence Relation

If the average of two successive years' production is .5(a_n-a_n-1) = 2n+5 and a₀=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?

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.