Find a sequence

**mahefo** · February 25th 2011, 01:53 AM

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.

**HallsofIvy** · February 25th 2011, 04:21 AM

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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