已知数列{An}是等差数列,Sn是其前n项的和,求证S6,S12-S6,S18-S12也成等差数列.

问题描述:

已知数列{An}是等差数列,Sn是其前n项的和,求证S6,S12-S6,S18-S12也成等差数列.

因为S(6)=6a(1)+6×5d/2=6a(1)+15dS(12)=12a(1)+66dS(18)=18a(1)+153d而S(12)-S(6)=6a(1)+51dS(18)-S(12)=6a(1)+87d可见,S(6)、S(12)-S(6)、S(18)-S(12)之间满足2[S(12)-S(6)]=S(6)+[S(18)-S(12)]即三者成等差数列....