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Sequence homework problem

  1. Jun 19, 2013 #1
    1. The problem statement, all variables and given/known data
    Let a be a real number such that 1 < a < 2 ,{an} is a sequence defined by
    a1=a, an+1=|an|-1 (n=1,2,3...)
    And put sn=a1+a2+a3+....an
    i)Find the a4,a5,a6,a7
    i)Find a4,a5,a6,a7

    3. The attempt at a solution
    I don't even know how to start.Maybe someone could give me an idea.
     
  2. jcsd
  3. Jun 19, 2013 #2

    haruspex

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    Try to write out the first few terms of the sequence.
     
  4. Jun 19, 2013 #3

    CompuChip

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    Maybe try picking a concrete a, like a = 3/2 or a = 4/3, and see how the sequence behaves?
     
  5. Jun 19, 2013 #4
    Okay I took a=1.25,then got:
    a1=1.25
    a2=0.25
    a3=-0.75
    a4=0.25
    a5=-0.75
    a6=0.25
    a7=-0.75
    I then tried to interpret that to get that
    a4 should be a-1 and a6 should be a-1 which are correct but for a5 and a7 I get the answer as 1-a for both but the answer should be a-2
     
  6. Jun 19, 2013 #5

    CompuChip

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    Check your a4.
    |-0.75| - 1 = ... ?
     
  7. Jun 19, 2013 #6
    Oh,..got it,.thanks.Okay
     
  8. Jun 19, 2013 #7

    CompuChip

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    OK now can you do it more generally, for a = 1 + r, where 0 < r < 1?
     
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