Question

已知等差数列｛an｝的前n项和为Sn,公差为d

求证：Sn,S2n-Sn,S3n-S2n,.....成等差数列。
书上是这样证的：S2n-Sn=an+1+an+2+....a2n
=(a1+nd)+(a2+nd)+...(an+nd)
…
请问“(a2+nd)”(an+nd)”“怎么来的啊

Answer 1

S2n-Sn=a(n+1)+a(n+2)+....a2n
an=a1+(n-1)d
a(n+1)=a1+nd
a(n+2)=a1+(n+1)d=a1+d+nd=a2+nd
.....

a(n+1)+a(n+2)+....a2n
=(a1+nd)+(a2+nd)+...(an+nd)

追问

a1+d怎么等于a2的啊？

追答

等差数列啊
a2-a1=d
a3-a2=d
....
d是公差哦

Answer 2

a2+nd就代表从第二项加n个差,因为是等差数列,就是说第n+2项了.