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How to solve recurrence relation with one real root and two complex roots ?

  1. Aug 24, 2010 #1
    How to solve recurrence relation with one real root and two complex roots ???

    The Example is ;

    Solve the recurrence relation a n-1 + a n-3 = 0 where n ≥ 3 and a 1 = 1 a 2 = 1 a 3 = 2
    a n = nth order
    a n-1 = (n-1)th order.
    a n-3 = (n-3)th order.

    I've started the solving ;
    a n = r^n
    so
    the equation will be ;

    r^n - r^(n-1) - r^(n-3)
    r^3 - r^2 - 1 = 0
    I could'nt do anything after find the roots ?
    What should i do ?
    Thanks for helping.
     
  2. jcsd
  3. Aug 24, 2010 #2

    jasonRF

    User Avatar
    Science Advisor
    Gold Member

    Re: How to solve recurrence relation with one real root and two complex roots ???

    I think you are making this harder than it is. Hint:

    you can rewrite you recurrence relation as

    [tex]
    a_{n} = - a_{n-2}.
    [/tex]

    So what is [tex]a_4[/tex]? How about [tex]a_5[/tex]? See the pattern?

    jason
     
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