>
数学
>
等比数列{a
n
}的前n项和为S
n
,已知S
1
,S
3
,S
2
成等差数列
(Ⅰ)求{a
n
}的公比q;
(Ⅱ)a
1
-a
3
=3,求S
n
.
人气:233 ℃ 时间:2019-08-18 16:06:52
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
1
q+
a
1
q
2
)=a
1
+a
1
+a
1
q,
解得q=-
1
2
或q=0(舍).
∴q=-
1
2
.
(Ⅱ)∵a
1
-a
3
=3,q=-
1
2
,
∴
a
1
−
1
4
a
1
=3
,a
1
=4,
∴
S
n
=
4[1−(−
1
2
)
n
]
1+
1
2
=
8
3
[1-(-
1
2
)
n
].
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