题目内容
等差数列
中,
,若数列
的前
项和为
,则
的值为
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165618159467.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165618174645.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165618237619.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165618252304.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165618268440.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165618252304.png)
A.18 | B.16 | C.15 | D.14 |
B
根据a3=8,a7=20等差数列的通项公式为3n-1,然后根据数列的前n项的和
Sn=
,
因为
=
(
)可得Sn=
解出n即可.
解:设等差数列的首项为a,公差为d,
因为a2=5,a6=17,所以a+d=5,a+5d=17,解得d=3,a=2.an=3n-1;
又因为
=
=
(
),
所以Sn=
(
)
=
(
-
)=25,解得n=16
故选B
Sn=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231656182991377.png)
因为
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165618315778.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165618330327.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165618346592.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165618440431.png)
解:设等差数列的首项为a,公差为d,
因为a2=5,a6=17,所以a+d=5,a+5d=17,解得d=3,a=2.an=3n-1;
又因为
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165618455488.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165618315778.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165618330327.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165618689648.png)
所以Sn=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165618330327.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231656187201139.png)
=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165618330327.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165618767338.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823165618830458.png)
故选B
![](http://thumb.zyjl.cn/images/loading.gif)
练习册系列答案
相关题目