证::n=1,a1=s1=4
n>1 an=Sn-Sn-1 Sn=n^2+3nSn-1=(n-1)^2+3(n-1)an=2n+2 经验证n=1满足通项
n>1
an-an-1=2,由等差数列定义可知,数列{an}是等差数列