# Math Help - Find a sequence

1. ## 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.

2. 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.