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.
人气:349 ℃ 时间:2019-08-22 11:41:27
解答
(Ⅰ)∵等比数列{a
n}的前n项和为S
n,
S
1,S
3,S
2成等差数列,
∴2(a
1+a
1q+
a1q2)=a
1+a
1+a
1q,
解得q=-
或q=0(舍).
∴q=-
.
(Ⅱ)∵a
1-a
3=3,q=-
,
∴
a1−a1=3,a
1=4,
∴
Sn==
[1-(-
)
n].
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