10Sn=an^2+5an+6 (1)10Sn-1=an-1^2+5an-1+6 (2)(1)-(2)整理得（an+an-1)(an-an-1-5)=0正项数列a=>an+an-1>0所以an-an-1-5=0，即数列a为等差数列，公差为5又a1*a15=(a3)^2 => a1=2故有an=5n-3
