等比数列{an}中,前n项和为sn,已知S1,S3,S2成等差数列,求{an}的公比Q 已知a1-a3=3,求sn?即2S3=S1+S?
问题描述:
等比数列{an}中,前n项和为sn,已知S1,S3,S2成等差数列,求{an}的公比Q 已知a1-a3=3,求sn?即2S3=S1+S?
答
2S3=S1+S22(a1+a2+a3)=2a1+a2a2+2a3=0a2(1+2q)=0 a2≠0∴q=-1/2
a1-a3=a1(1-q^2)=3 ∴ a1=4
∴sn=a1(1-q^n)/(1-q)=3/8*[1-(-2)^(-n)]