问题描述: 设{an}是公比不等于1的等比数列,Sn是其前n项和,若a1,2a7,3a4成等差数列,求证12S3,S6,S12-S6成等比数列 1个回答 分类:数学 2014-10-17 问题解答: 我来补答 q=公比≠1a7=a4q^34a7=a1+3a4=4a4q^3a4=a1/(4q^3-3)=a1q^3,Q=q^31=(4Q-3)Q=4Q^2-3Q4Q^2-3Q-1=0(4Q+1)(Q-1)=0Q=-1/4q=(-1/4)^(1/3)令z=1-q12S3=12a1(1-q^3)/(1-q)=15a1/(1-q)=15a1/zS6=a1(1-1/16)/(1-q)=15a1/16zS12-S6=(a1/z)[1-1/16^2-1+1/16]=(a1/z)*15/16^2S6/12S3=[(a1/z)*15/16]/15(a1/z)=1/16(S12-S6)S6=(15/16^2)/(15/16)=1/16=S6/12S3所以,12S3,S6,S12-S6成等比数列 展开全文阅读