题目内容
已知数列
的前4项和等于4,设前n项和为
,且
时,
,则
.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135021362507.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135021378395.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135021394448.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135021409978.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135021425424.png)
25
先由an=sn-sn-1(n≥2)以及an=![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135021440338.png)
(n≥2)得到
,所以{
}是等差数列,再由s4=4就可求出S10=25
解:∵n≥2时,an=sn-sn-1,又
∴sn-sn-1=
∴![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135021472678.png)
∴{
}是等差数列,公差为![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135021440338.png)
∴
=2+3=5
∴s10=25
答案为:25
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135021440338.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135021456691.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135021472678.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135021487463.png)
解:∵n≥2时,an=sn-sn-1,又
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135021409978.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135021518855.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135021472678.png)
∴{
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135021487463.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135021440338.png)
∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135021643823.png)
∴s10=25
答案为:25
![](http://thumb.zyjl.cn/images/loading.gif)
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