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How do we get the n th term of the sequence?

  1. Sep 16, 2014 #1
    1. The problem statement, all variables and given/known data

    how do we get the n th term of a sequence if it is given in form of
    ##x_{ n+1 }=f({ x }_{ n })##
    and the p th term is given

    2. Relevant equations
    I figured we may get it if we get it in the form of
    ##x_{ n+1 }-{ x }_{ n }## but how?can we even get it?if yes,under what conditions?
    3. The attempt at a solution
    example: n th term of sequence where
    ##x_{ n+1 }=\frac { { x }_{ n }+\frac { 2 }{ { x }_{ n } } }{ 2 } ##
    where ##{ x }_{ 0 }=1##
     
    Last edited: Sep 16, 2014
  2. jcsd
  3. Sep 16, 2014 #2

    pasmith

    User Avatar
    Homework Helper

    Non-linear recurrences are unlikely to have solutions in closed form. Iteration is generally the only way to find [itex]x_n[/itex] given [itex]x_0[/itex].
     
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