题目
题型:不详难度:来源:
(1)求数列{an}的通项公式;
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073644-83839.png)
答案
解析
试题分析:(1)解 设等比数列{an}的首项为a1,公比为q.依题意,有2(a3+2)=a2+a4,代入a2+a3+a4=28,可得a3=8,∴a2+a4=20,所以
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073644-82925.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073644-11590.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073644-70689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073645-29081.png)
Sn=2+22+23+…+2n-n·2n+1=2n+1-2-n·2n+1.要使Sn+n·2n+1>50,即2n+1-2>50,即2n+1≥52.
易知:当n≤4时,2n+1≤25=32<52;当n≥5时,2n+1≥26=64>52.故使Sn+n·2n+1>50成立的正整数n的最小值为5.
点评:主要是考查了等比数列的通项公式和求和的运用,属于基础题。
核心考点
试题【已知单调递增的等比数列{an}满足:a2+a3+a4=28,且a3+2是a2,a4的等差中项.(1)求数列{an}的通项公式;(2)若,Sn=b1+b2+…+b】;主要考察你对等比数列等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073634-57959.png)
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![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073635-66379.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073634-57959.png)
(2)设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073635-69947.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073636-99244.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073635-59384.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073636-34747.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073636-88143.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073623-46985.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073623-77735.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073624-49163.png)
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![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073624-14033.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073623-46985.png)
(2)试推导数列
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073624-94186.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073623-77735.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073625-75152.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073613-61053.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073614-42545.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073614-22802.png)
(1) 求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073613-61053.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073614-13519.png)
(2) 记
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073614-22003.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073615-31799.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073615-61036.png)
(3) 记
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073615-38387.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073615-61036.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073615-49387.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073615-20563.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073602-24468.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073602-97971.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073602-79562.png)
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A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073522-78555.png)
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![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073522-65445.png)
(Ⅰ)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073522-78555.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073522-41542.png)
(Ⅱ)记
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073523-64772.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014073523-16546.png)
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