Sn为数列{an}的前n项和，已知an>0,且an^2+an=4Sn+3。求an通项公式。

4Sn=an^2+2an-3 4S1=a1^2+2a1-3 a1=1 4Sn-1=an-1^2+2an-1-3 4an=an^2-an-1^2+2an-2an-1 an^2-an-1^2-2an-2an-1=0 (an+an-1)(an-an-1-2)=0 an=an-1+2 an=1+(n-1)*2=2n-1