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Linear recurrence = closed form?

  1. Apr 5, 2013 #1
    Hi

    I've got a recurrence relation: x_n = a*x_(n-1) + b;

    I think I'm going mad trying to figure out a closed form, eg. x(n) = ? the nth iteration

    Is there a trick or something I'm missing?

    Thanks
     
  2. jcsd
  3. Apr 5, 2013 #2

    jbunniii

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    Try writing out what you get for ##x_1##, ##x_2##, ##x_3## and see what the pattern is. Then take an educated guess and try to prove it by induction.
     
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