在数列{an}中,a(n+1)=an+2n,a1=2,则a100=?
问题描述：
在数列{an}中,a(n+1)=an+2n,a1=2,则a100=?
a(n+1)指第n+1项
答
∵a(n+1)=an+2n∴a(n+1)-an=2n (1)an-a(n-1)=2(n-1)=2n-2 (2)a(n-1)-a(n-2)=2(n-2)=2n-4.a3-a2=2×2=4=2n-2n+4a2-a1=2=2n-2n+2 (n)(1)+(2)+.+(n)得:an-a1=n×(2n)+{n(0+[-2(n-1)])/2} =(n^2)-na100=100^2-100+2=1000...