已知数列{an},其前n项和为sn,且sn=n2+n,则通项公式an=_.
问题描述:
已知数列{an},其前n项和为sn,且sn=n2+n,则通项公式an=______.
答
∵数列{an},其前n项和为sn,且sn=n2+n,
∴当n≥2时,sn-1=(n-1)2+(n-1),
∴an=sn-sn-1=(n2+n)-[(n-1)2+(n-1)]=2n;
当n=1时,a1=s1=1+1=2,满足an;
∴数列的通项公式为an=2n,n∈N*.
故答案为:2n,n∈N*.