an-a(n-1)=n+2a(n-1)-a(n-2)=(n-1)+2……a3-a2=3+2a2-a1=2+2加起来,左边中间正负抵消an-a1=(2+3+……+n)+2(n-1)=[n(n+1)/2-1]+2(n-1)=n^2/2+n/2-1+2n-2=n^2/2+5n/2-3a1=3an=n^2/2+5n/2=n(n+5)/2