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Math Help - sequences problem.

  1. #1
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    sequences problem.

    We have these two sequences, defined as:

    Xn+1= Xn + Yn and Yn+1=Xn-Yn

    and X0=Y0=1.

    Find simple formulae for Xn and Yn. Don't even know how to start this... any help is welcome. I know it must be simple, but don't know how to do it. Usual difference equations I had were x smth and then I could use lambda exchange and find coefficients to solve it. This I don't know.
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  2. #2
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    Quote Originally Posted by fiksi View Post
    We have these two sequences, defined as:
    Xn+1= Xn + Yn and Yn+1=Xn-Yn and X0=Y0=1.
    Here are 16 terms of the sequence. See if you can find a pattern.
    Attached Thumbnails Attached Thumbnails sequences problem.-seq5.gif  
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  3. #3
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    Quote Originally Posted by Plato View Post
    Here are 16 terms of the sequence. See if you can find a pattern.
    Well, then I'd have "guesswork" which wouldn't be rigorous enough for my teacher...
    It looks as if I need a precise method here...
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  4. #4
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    Quote Originally Posted by fiksi View Post
    Well, then I'd have "guesswork" which wouldn't be rigorous enough for my teacher...It looks as if I need a precise method here...
    Well OK! I will give you the y-sequence.
     y_n  = \left( { - 1} \right)^n  \cdot 2^{\left\lfloor {\frac{n}{2}} \right\rfloor } where {\left\lfloor {\frac{n}{2}} \right\rfloor } is the floor function (greatest integer).

    Now you try the x-sequence. Hint it involves the mod(2) function.
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