1 . 把正整数排列成如图甲三角形数阵,然后擦去第偶数行中的奇数和第奇数行中的偶数,得到如图乙的三角形数阵,再把图乙中的数按从小到大的顺序排成一列,得到一个数列
,若
,则![](https://img.xkw.com/dksih/QBM/2010/5/24/1569746030387200/1569746035662848/STEM/8e26904db10747f4a94bdcb38e944092.png?resizew=21)
______________ .
![](https://img.xkw.com/dksih/QBM/2012/7/25/1570936299487232/1570936304910336/STEM/d69d365e8fa042528e9a83dc59d6cffa.png?resizew=340)
![](https://img.xkw.com/dksih/QBM/2012/7/25/1570936299487232/1570936304910336/STEM/383f232e8aeb49069cefa2b0c65159d0.png?resizew=340)
![](https://img.xkw.com/dksih/QBM/2010/5/24/1569746030387200/1569746035662848/STEM/f2e170bbcded47f996f45f1bef4b3b08.png?resizew=26)
![](https://img.xkw.com/dksih/QBM/2010/5/24/1569746030387200/1569746035662848/STEM/4e4c6a26122b4011972ac749bd7c9c51.png?resizew=62)
![](https://img.xkw.com/dksih/QBM/2010/5/24/1569746030387200/1569746035662848/STEM/8e26904db10747f4a94bdcb38e944092.png?resizew=21)
![](https://img.xkw.com/dksih/QBM/2012/7/25/1570936299487232/1570936304910336/STEM/d69d365e8fa042528e9a83dc59d6cffa.png?resizew=340)
![](https://img.xkw.com/dksih/QBM/2012/7/25/1570936299487232/1570936304910336/STEM/383f232e8aeb49069cefa2b0c65159d0.png?resizew=340)
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2016-12-01更新
|
595次组卷
|
7卷引用:2012届上海市长宁区高三教学质量测试理科数学
(已下线)2012届上海市长宁区高三教学质量测试理科数学(已下线)湖北省黄冈中学2010届高三5月第二次模拟考试数学试题(理科)(已下线)2010年湖北省黄冈中学高三第三次模拟考试(理科)数学卷(已下线)2012届河南省豫南九校高三第四次联考理科数学上海市南洋模范中学2018-2019学年高一下学期期末数学试题(已下线)2011-2012学年浙江省余姚市三校高二下学期第二次月考理科数学试卷贵州省铜仁市思南中学2020-2021学年高二下学期期中考试数学(文)试题
2 . 由下面四个图形中的点数分别给出了四个数列的前四项,将每个图形的层数增加可得到这四个数列的后继项.按图中多边形的边数依次称这些数列为“三角形数列”、“四边形数列”…,将构图边数增加到n可得到“n边形数列”,记它的第r项为P(n,r).
![](https://img.xkw.com/dksih/QBM/2012/4/2/1570827002732544/null/STEM/60ef9a9405364ef8864019f7a3b9eb6b.png?resizew=517)
(1)求使得P(3,r)>36的最小r的取值;
(2)试推导P(n,r)关于n、r的解析式;
(3)是否存在这样的“n边形数列”,它的任意连续两项的和均为完全平方数.若存在,指出所有满足条件的数列,并证明你的结论;若不存在,请说明理由.
![](https://img.xkw.com/dksih/QBM/2012/4/2/1570827002732544/null/STEM/60ef9a9405364ef8864019f7a3b9eb6b.png?resizew=517)
(1)求使得P(3,r)>36的最小r的取值;
(2)试推导P(n,r)关于n、r的解析式;
(3)是否存在这样的“n边形数列”,它的任意连续两项的和均为完全平方数.若存在,指出所有满足条件的数列,并证明你的结论;若不存在,请说明理由.
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2012·上海长宁·一模
3 . 已知
是等差数列,
,其前10项和
,则其公差![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c98c59cd4749afdd21e73529fc84323.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d958eca33659a443e15d05dc7310980.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7ab17eae9740e2576f56fd415156b52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c98c59cd4749afdd21e73529fc84323.png)
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2012·上海嘉定·一模
4 . 在等差数列{an}中,
,
,则{an}的前10项和S10=__________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/451eb590e9d37c9198f9fe91e03775b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ecf6dcaeefb5a4d19a6a646cc4a5bc0.png)
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2011·广东广州·一模
名校
解题方法
5 . 已知数列
是等差数列, 若
, 则该数列前11项的和为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38db56f3afda4b5e5365014c9d581d34.png)
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2010·上海普陀·二模
6 . 已知数列
的首项为1,前
项和为
,且满足
,
.数列
满足
.
(1) 求数列
的通项公式;
(2) 当
时,试比较
与
的大小,并说明理由;
(3) 试判断:当
时,向量![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1f6486933fe3c2459cb13943244a088.png)
是否可能恰为直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a461995b90655f5133df6f61c2d09bd.png)
的方向向量?请说明你的理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5995ed803c917b995c197681464f2570.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b987d8d20701991392200fa311cd2814.png)
(1) 求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2) 当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe3c7a8aa20a4d8f59e069331588a8bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab771f88ee47a186de5e80f557171453.png)
(3) 试判断:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1f6486933fe3c2459cb13943244a088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c2b289b20ecde54bf91c3a0bd5869e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a461995b90655f5133df6f61c2d09bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e091cface0c4a22727634eb480562d6.png)
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2010·上海普陀·二模
7 . 某企业投资72万元兴建一座环保建材厂. 第1年各种经营成本为12万元,以后每年的经营成本增加4万元,每年销售环保建材的收入为50万元. 则该厂获取的纯利润达到最大值时是在第______ 年.
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2010·上海普陀·一模
8 . (理)已知等差数列
的公差是
,
是该数列的前
项和.
(1)试用
表示
,其中
、
均为正整数;
(2)利用(1)的结论求解:“已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31fa241aa355a70708f6caaee10de675.png)
,求
”;
(3)若数列
前
项的和分别为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a76d38e317b8d95ec86e3159fb79572.png)
,试将问题(1)推广,探究相应的结论. 若能证明,则给出你的证明并求解以下给出的问题;若无法证明,则请利用你的研究结论和另一种方法计算以下给出的问题,从而对你猜想的可靠性作出自己的评价.问题:“已知等差数列
的前
项和
,前
项和
,求数列
的前2010项的和
.”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd015442628054692b8cc0a19c77d2bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)试用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1cc620d2e9376f14d923748ab928d5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef508e397e53ca005a367bfec4028d35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)利用(1)的结论求解:“已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31fa241aa355a70708f6caaee10de675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00fa2bbedb9af80857d9c92bb86f0986.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef508e397e53ca005a367bfec4028d35.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd015442628054692b8cc0a19c77d2bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/697e84689167caa36ac89184035aab56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a76d38e317b8d95ec86e3159fb79572.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e36444a54460e7942f04883b7dd2c270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd015442628054692b8cc0a19c77d2bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2639c64902dae0fc4d735e8020ea8e38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b7f27ebcef70a3ebbbe8d2e53ea0896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa561fcad46eaf8d841efa58fe9a8af2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd015442628054692b8cc0a19c77d2bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/258cb9187f4d464ba98ccd9eff1b89fc.png)
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2010·上海普陀·一模
9 . (文)已知等差数列
的公差是
,
是该数列的前
项和.
(1)求证:
;
(2)利用(1)的结论求解:“已知
、
,求
”;
(3)若各项均为正数的等比数列
的公比为
,前
项和为
.试类比问题(1)的结论,给出一个相应的结论并给出证明.并利用此结论求解问题:“已知各项均为正数的等比数列
,其中
,
,求数列
的前
项和
.”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd015442628054692b8cc0a19c77d2bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0242e98ae52be08247a7cd2bafd806d.png)
(2)利用(1)的结论求解:“已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2639c64902dae0fc4d735e8020ea8e38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa561fcad46eaf8d841efa58fe9a8af2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d16765bfe96c4c2733afdf4099a33f5e.png)
(3)若各项均为正数的等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/503d69ae8f4e42d5ca6fd003327f30fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2639c64902dae0fc4d735e8020ea8e38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa561fcad46eaf8d841efa58fe9a8af2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df0096ced57c6f31f2e0fe402bd56334.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e6f1af4b44b2e97e8f319bab4ae9010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a34a901aa78366ac960f5f4e7f1fcbac.png)
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