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Math Help - Solution of Inhomogeneous Recurrence Relation

  1. #1
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    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?
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  2. #2
    MHF Contributor MarkFL's Avatar
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    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.
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