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?