(an+1-1)(an-1)=3(an-an+1),等价为(an+1-1)(an-1)=3[(an-1)-(an+1-1)],∴1an+1-1-1an-1=13,即数列{1an-1}是等差数列,首项为1a1-1=12-1=1,公差d=13,则1an-1=1+13(n-1)=n+23,则an-1=3n+2,即an=1+3n+2=n+5n+2.