已知数列{an}是等差数列,Sn是其前几项的和,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是其前几项的和,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+87d2(S12-S6)=2*(6a1+51d )=12a1+102dS18-S12+S6=6a1+87d+6a1+15d=12a1+102d...