Question

等比数列{An}的公比为q,前n项和为Sn,且S3,S9,S6成等差数列,求q的值

Answer 1

当q不等于1时,Sn=a1(1-q^n)/(1-q),S3=a1(1-q^3)/(1-q) ,S9=a1(1-q^9)/(1-q),

S6=a1(1-q^6)/(1-q),且2S9=S3+S6,带入消去a1,1-q,得：2-2*q^9=2-q^3-q^6

所以,2*q^6-q^3-1=0,令q^3=t,则2*t^2-t-1=0,所以t=-1/2 或1（舍去）

当q=1时,An=c(常数),2S9=2*9c=S3+S6=3c+6c,所以c=0,