在等差数列{an}中,已知Sn,S2n,S3n分别表示数列的前n项和,前2n项和,前3n项和.求证:Sn,S2n-Sn,S3n-S2n是等差
问题描述：
在等差数列{an}中,已知Sn,S2n,S3n分别表示数列的前n项和,前2n项和,前3n项和.求证:Sn,S2n-Sn,S3n-S2n是等差
答
Sn=a1n+n(n-1)d/2
S2n=a1*2n+2n(2n-1)d/2
S3n=a1*3n+3n(3n-1)d/2
S2n-Sn=a1*n+n(4n-2-n+1)d/2=a1n+n(3n-1)d/2
S3n-S2n=a1n+n(9n-3-4n+2)d/2=a1n+n(5n-1)d/2
(S2n-Sn)-Sn=(S3n-S2n)-(S2n-Sn)
等差