数列{An}是等比数列Sn是前n项和,A1,A7,A4成等差数列求证2S3,S6,S12-S6成等比数列
问题描述：
数列{An}是等比数列Sn是前n项和,A1,A7,A4成等差数列求证2S3,S6,S12-S6成等比数列
答
a7=a1q^6 a4=a1q^3 因为a1,a7,a4成等差数列 所以a7=(a1+a4)/2 a1q^6=(a1+a1q^3)/2 2q^6-q^3-1=0 (2q^3+1)(q^3-1)=0 q^3=1,或q^3=-1/2 因为 2S3=2a1(1-q^3)/(1-q) S6=a1(1-q^6)/(1-q) S12-S6=a1(1-q^12)/(1-q)-a1(1-q...