CN-LEAGUE 2011 Problem 10

A sequence $a_n$ satisfies $a_1 =2t-3$ ( $t \ne 1,-1$ ), and $a_{n+1}=\dfrac{(2t^{n+1}-3)a_n+2(t-1)t^n-1}{a_n+2t^n-1}$ . [list]i) Find $a_n$ ,ii) If $t>0$ , compare $a_{n+1}$ with $a_n$ .[/list]