等比数列{an}的前n项和为Sn,已知S1,S3,S2成等差数列 (Ⅰ)求{an}的公比q; (Ⅱ)a1-a3=3,求Sn.
问题描述:
等比数列{an}的前n项和为Sn,已知S1,S3,S2成等差数列
(Ⅰ)求{an}的公比q;
(Ⅱ)a1-a3=3,求Sn.
答
(Ⅰ)∵等比数列{an}的前n项和为Sn,
S1,S3,S2成等差数列,
∴2(a1+a1q+a1q2)=a1+a1+a1q,
解得q=-
或q=0(舍).1 2
∴q=-
.1 2
(Ⅱ)∵a1-a3=3,q=-
,1 2
∴a1−
a1=3,a1=4,1 4
∴Sn=
=4[1−(−
)n]1 2 1+
1 2
[1-(-8 3
)n].1 2