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Finding closed form of sequence.

  1. Nov 13, 2013 #1
    1. The problem statement, all variables and given/known data

    {U_0 = 9, U_1 = -3}

    U_(n+2) = -(5/4) U_(n+1) + (3/8) U_(n)

    2. Relevant equations



    3. The attempt at a solution

    First step was to attempt to find the common difference by trying to find the 3rd term:

    U_(2) = -(5/4) u_(1) + 3/8 U_(0) = -(57/8)

    This does not give a common difference, I was expecting -1/3

    I feel I have gone wrong somewhere, help would be greatly appreciated!
     
  2. jcsd
  3. Nov 13, 2013 #2

    pasmith

    User Avatar
    Homework Helper

    You have a sign error; (-5/4)(-3) + (3/8)(9) = 57/8.

    Why do you expect it to?

    The method of solving such linear recurrence relations is to look for a solution of the form [itex]u_n = A\lambda_1^n + B\lambda_2^n[/itex]. If you substitute this into the recurrence relation you will find that [itex]\lambda_1[/itex] and [itex]\lambda_2[/itex] are solutions of the same quadratic equation. The given values for [itex]u_0[/itex] and [itex]u_1[/itex] will then enable you to find [itex]A[/itex] and [itex]B[/itex].
     
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