已知数列〔an〕是等差数列,sn是前n项之和,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是前n项之和,求证s6,s12_s6,s18-s12也成等差数列
答
S6=(a1+a6)*6/2 =3(a1+a6)=6a1+15d
S12-S6=(a1+a12)*12/2-(a1+a6)*6/2
= 6(a1+a12)-3(a1+a6)
= 3a1+6a12-3a6
= 6a1+51d
同理
S18-S12=6a1+87d
2(S12-S6)=2*(6a1+51d )=12a1+102d
S18-S12+S6=6a1+87d+6a1+15d=12a1+102d
所以S6,S12-S6,S18-S12也成等差数列
不懂的欢迎追问,非常谢谢，我会了不客气.如果满意的话麻烦及时采纳，谢谢了!