1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    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].
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Finding closed form of sequence.
  1. Closed Form Summation (Replies: 2)

  2. Closed Form Summation (Replies: 15)