Question

等比数列{an}的前n项和为Sn,已知S1,S3,S2成等差数列

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

Answer 1

1.
2S3=S1+S2
2(a1+a1q+a1q²)=a1+a1+a1q
整理渣侍裤，得2q²+q=0
q(2q+1)=0
q=0(舍去)或q=-1/2
q=-1/2
2.
a1-a3=-3/2
a1(1-q²)=-3/2
a1=(-3/2)/(1-q²)
q=-1/2代入，得
a1=(-3/2)/如简[1-(-1/2)²]=-2
Sn=a1(1-qⁿ)/(1-q)
=(-2)[1-(-1/谈羡2)ⁿ]/[1-(-1/2)]
=(-4/3)[1-(-1/2)ⁿ]