Question

等比数列{an}的前n项和为Sn,已知S1,S2,S3成等差数列 (1)求{an}的公比q (2)若a1-a3=3,求S

Answer 1

(1)S1=a1;S2=a1(1+q);S3=a1(1-q^3)/(1-q)=a1(1+q+q^2) (分母不为0,得q≠1)

又2S2=S1+S3 化简后得q=0

(2)a1-a3=a1(1-q^2)=3 得a1=3 则Sn=3(1-q^n)/(1-q)=3

可判断{an}是首项为3,其余各项为0的等比数列