1 . 已知等差数列
的前n项和为
,
,
,数列
满足
,
.
(1)求
的通项公式;
(2)设数列
满足
,若
的前n项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/033fd16b5cffcaf285d28d7583e0ff3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b72ddd7de598464a37b10f03f67b904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0ce1a0815e84c82544abd418572f4b6.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89018baf5e950b99d0f1d3a48f6d688.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2caf8c4806569a493c79902a617f4c2e.png)
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4卷引用:山东省临沂市2023-2024学年高三上学期期中考试数学试题
山东省临沂市2023-2024学年高三上学期期中考试数学试题新疆克拉玛依市第十三中学2024届高三上学期12月月考数学试题(已下线)第四章 数列(压轴题专练,精选28题)-2023-2024学年高二数学单元速记·巧练(人教A版2019选择性必修第二册)山西省太原市成成中学校2023-2024学年高二下学期4月月考数学试题
2 . 已知数列
满足
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/060c880252326cb449d8253539d92aff.png)
(1)判断数列
是否是等比数列?若是,给出证明;否则,请说明理由;
(2)若数列
的前10项和为361,记
,数列
的前n项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/390636a89883bd64bf8da9bf8654aff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/060c880252326cb449d8253539d92aff.png)
(1)判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf33b2a94eae16760d746f9b4b8dbc.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04053ecf80b3bb9179c8baab47bf8dae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffc0cf1f0a00718b95a2a4fffd11dd32.png)
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9卷引用:山东省济宁市泗水县2024届高三上学期期中数学试题
3 . 给定无穷数列
,若无穷数列
满足:对任意
,都有
,则称
与
“接近”,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3dd644fc0373b59f11179da6a242bed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
A.设![]() ![]() ![]() |
B.设 ![]() ![]() ![]() ![]() |
C.设数列![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
D.已知![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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解题方法
4 . 已知四边形ABCD,
为边BC边上一点,连接
交BD于
,点
满足
,其中
是首项为1的正项数列,
,则
的前n项![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7978d7bd6f6caf9ac9837ffce5f89654.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8afeb8186b086048780bc0ed828fb534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acd7a30b45915f624fc0b658537d97c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/436761021d45e52795bce14caf372d7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a78b3c84e7818ed70018eea40c72665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd5d42a4f61ed0ed58e63d15c9445d88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bd786c52f9bd6e82d069cc319992cef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c80a89109f332a04f12dcc41e010e7cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7978d7bd6f6caf9ac9837ffce5f89654.png)
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5卷引用:山东省青岛市即墨区2023届高三上学期期中数学试题
山东省青岛市即墨区2023届高三上学期期中数学试题辽宁省沈阳市新民市高级中学2023-2024学年高三上学期10月月考数学试题(已下线)专题4-2向量四心及补充定理综合归类-1江苏省常州市第一中学2024届高三下学期期初检测数学试题(已下线)【练】 专题三 平面向量与其他知识的交汇问题(压轴大全)
名校
5 . 引得无数球迷心情澎湃的世界杯,于今年在卡塔尔举行,为了弘扬顽强拼搏的体育竞技精神,某学校的足球社团利用课余时间展开“三人足球”的比赛,比赛的第一阶段为“传球训练赛”,即参赛的甲、乙、丙三名同学,第一次传球从乙开始,随机地传球给其他两人中的任意一人,接球者再随机地将球传给其他两人中的任意一人,则第6次传球,重新由乙同学传球的概率为___________ .
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7卷引用:山东省青岛第一中学2023-2024学年高二下学期第一次模块考试数学试题
山东省青岛第一中学2023-2024学年高二下学期第一次模块考试数学试题湖北省荆州市八县市2022-2023学年高二上学期期末联考数学试题湖北省黄冈市红安县第一中学2022-2023学年高二上学期元月考试数学试题(已下线)江西省上饶市2023届高三第一次高考模拟考试数学(理)试题变式题16-20(已下线)第三篇 数列、排列与组合 专题1 建立递推关系求通项公式 微点2 建立递推关系求通项公式综合训练(已下线)第七节 二项分布、超几何分布与正态分布 A卷素养养成卷 一轮点点通(已下线)专题20 概率与统计常考小题归类(15大题型)(练习)
6 . 将
个数排成
行
列的数阵,如图所示:该数阵第一列的
个数从上到下构成以
为公差的等差数列,每一行的
个数从左到右构成以
为公比的等比数列(其中
0).已知
,记这
个数的和为
,下面叙述正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4220a7e39a57c9467a9b17b96eff3de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ceef1abeeef220b4fe5f7d96feedd90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1acee0663e9381923a9e0d9fe0c1809.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31aa2af2c2cebc830d131ae8b812d15a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ceef1abeeef220b4fe5f7d96feedd90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4220a7e39a57c9467a9b17b96eff3de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
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解题方法
7 . 在平面四边形ABCD中,点D为动点,
的面积是
面积的2倍,又数列
满足
,恒有
,设
的前n项和为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11803522bc55106e15361d8c3feb6c24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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6卷引用:山东省聊城市2022-2023学年高三上学期期中数学试题
8 . 已知
轴上的点
、
、…、
满足
,射线
上的点
、
、…、
满足
,
,则四边形
的面积
的取值范围为______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e92b8041e98e4f435acdbeb983efbe46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5755123f876868394b160608317eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b25286f6029da66ce5270aacd05184f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2206925716403c243a10f6c534392a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e49f0172de00b37e1f3861a751a57dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5da0eb3662f64f56c090473cbabb4814.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/420f40c58d5518aea8e83a99074807d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c65433a22b15ea4e75432d74a1ccf3b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/687bbc662e93519ef9acc477935d7005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1505d56f0b35fe7f2de1fe1888036e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46bc1dfb9a0c62a95db470d4748fd35c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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4卷引用:山东省日照市校际联考2021-2022学年高二下学期期中数学试题
名校
解题方法
9 . 将正三角形(1)的每条边三等分,并以中间的那一条线段为底边向外作正三角形,然后去掉底边,得到图(2);将图(2)的每条边三等分,并以中间的那一条线段为底边向外作正三角形,然后去掉底边,得到图(3);如此类推,将图(
)的每条边三等分,并以中间的那一条线段为底边向外作三角形,然后去掉底边,得到图
.上述作图过程不断的进行下去,得到的曲线就是美丽的雪花曲线.若图(1)中正三角形的边长为1,则图(
)的周长为__________ ,图(
)的面积为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aceb113626093e0e431f30fa45c2c444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/cc4bbbc0-a228-404d-981c-94e842b746b2.png?resizew=216)
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6卷引用:山东省青岛市青岛第五十八中学2021-2022学年高三上学期期中数学试题
解题方法
10 . 已知数列
的前
项和为
,且
.
(1)求
的通项公式;
(2)在
与
之间插入
个数,使这
个数组成一个公差为
的等差数列,在数列
中是否存在3项
,
,
(其中
,
,
成等差数列)成等比数列?若存在,求出这样的3项;若不存在,请说明理由.
![](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/c8370a173854471a3eb27637993a3d5d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3468a665ac713ab7b400c672f19650a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e260b088f071983f254ce8f5163fcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee8598379ec01edc16c72c1d3fa3ce81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8904e7018ec79c8b0efdcb3ba67cb7cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2554efe1860dc6c769c34d8cfa6de3e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
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2卷引用:山东省临沂市2020-2021学年高三上学期期中考试数学试题