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Math Help - Find a sequence

  1. #1
    Junior Member
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    Find a sequence

    Can you help me this problem: "Find a sequence {x_n} satisfy: x_{2n+1}=3x_n +2\quad \forall n=0,1,2,\ldots ". Thanks to your help.
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  2. #2
    MHF Contributor

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    Why not just "write down" a sequence using those conditions? There are, of course, an infinite number of such sequences. That formula says nothing about even indices so we can just set them to be 0.

    If we take a_1= 0, a_2= 0 (just because it is simplest), Then x_3= x_{2(1)+1}= 3(0)+ 2= 2, x_4= 0, x_5= x_{2(2)+ 1}= 3(0)+ 2= 2, x_6= 0, x_7=x_{2(3)+ 1}= 3(2)+ 2= 8, x_8= 0, [tex]x_n= x_{2(4)+ 2= 2, x_{10}= 0, etc.
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