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

(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=-

1
2
或q=0(舍).
∴q=-
1
2

(Ⅱ)∵a1-a3=3,q=-
1
2

a1
1
4
a1=3
,a1=4,
Sn
4[1−(−
1
2
)n]
1+
1
2
=
8
3
[1-(-
1
2
n].