一直Sn是等比数列{an}的前n项和,S3 S9 S6成等差 求证a2 a8 a5成等差
问题描述：
一直Sn是等比数列{an}的前n项和,S3 S9 S6成等差 求证a2 a8 a5成等差
答
s3=a1(1-q^3)/(1-q) s9=a1(1-q^9)/(1-q) s6=a1(1-q^6)/(1-q) 2s9=s3+s6 2a1(1-q^9)/(1-q)=a1(1-q^3)/(1-q)+a1(1-q^6)/(1-q) 2(1-q^9)=(1-q^3)+(1-q^6) 2q^9-q^3-q^6=0 q^3(2q^6-q^3-1)=0 2q^6-q^3-1=0 2q^6-q^3-1=0 ...