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.
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.