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Math Help - homogeneous recurrence

  1. #1
    Junior Member
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    homogeneous recurrence

    I've come this far:

    an = 4an-1 + 5an-2

    a1 = 2
    a2 = 6

    roots
    x1 = 5
    x2 = -1

    I insert roots in : an = U*s1^n + V*s2^n

    which gives : an = 4*5^n + 5*(-1)^n

    what now?

    an could e.g. be a1?
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  2. #2
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    Hello Madspeter
    Quote Originally Posted by Madspeter View Post
    I've come this far:

    an = 4an-1 + 5an-2

    a1 = 2
    a2 = 6

    roots
    x1 = 5
    x2 = -1

    I insert roots in : an = U*s1^n + V*s2^n Correct, except that you mean x1 and x2 - see below

    which gives : an = 4*5^n + 5*(-1)^n No

    what now?

    an could e.g. be a1?
    Thanks for showing us your working so far. What you mean is:

    a_n = U{x_1^n} + V{x_2^n} = U.5^n +V.(-1)^n

    Then plug in the values n = 1, n = 2:

    a_1 = 2= 5U -V

    a_2 = 6 = 25U + V

    Can you complete it now?

    Grandad
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