2024高三·全国·专题练习
1 . 掷一枚质地均匀的骰子,得分规则如下:若出现的点数为1,则得1分;若出现的点数为2或3,则得2分;若出现的点数为4或5或6,则得3分.
(1)记
为连续掷这枚骰子2次的总得分,求
的数学期望;
(2)现在将得分规则变更如下:若出现的点数为1或2,则得2分,其他情况都得1分.反复掷这枚骰子,设总得分为
的概率为
,证明:数列
为等比数列.
(1)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(2)现在将得分规则变更如下:若出现的点数为1或2,则得2分,其他情况都得1分.反复掷这枚骰子,设总得分为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef65559a6b44930addc23adeb8d854c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8e5134f738fa09b1c307fe7612a4022.png)
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2024高三·全国·专题练习
2 . 已知等差数列
的前n项和为
,数列
是等比数列,
,
,
.
(1)求
与
;
(2)设
,求数列
的前n项和
.
![](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/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebaf2a2590bb84d646957f913d78f6dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4222cfed122540c95432295a14e6eab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43211db0a37826603234214efb060e44.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/019fc326211e8775d3393fc2c36c20a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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2024高三下·全国·专题练习
3 . 已知
为正项数列
的前
项积,且
,
.
(1)证明:数列
是等比数列;
(2)若
,
的前
项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](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/c0c9c5e687d303671da095ac09897fe1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f409148489b3a312b3644264ac96350c.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d108a155642da837f7af5c44ad7e27e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4fe99ae7973f47829463638c2c4b563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c4294f755303e36f223a9ce3dfc642a.png)
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4 . 设
为等差数列
的前n项和,且
,数列
满足
.
(1)求
和
的通项公式;
(2)若将数列
和
的公共项按从小到大的顺序组成一个新的数列
,求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe98f14c62e8389b61417fa45e9f7f23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0591a62663b8b4918b3fad8de982396b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若将数列
![](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/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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5 . 已知等差数列
的公差为d(
),前n项和为
,且满足
;
,
,
成等比数列.
(1)求数列
的通项公式;
(2)设
,数列
的前n项和为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/812be9806122241c476ba1db516c4823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/710c22735357979043c7cb1cf5e04350.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5da4cd81500bdb43118150dbdb1541e6.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/216876de04325fd250c38c485cbc34b7.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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2024-05-04更新
|
1779次组卷
|
8卷引用:第18题 数列不等式变化多端,求和灵活证明方法多(优质好题一题多解)
(已下线)第18题 数列不等式变化多端,求和灵活证明方法多(优质好题一题多解)(已下线)第18题 等差等比综合考查,生成数列通项求和(优质好题一题多解)河南省百师联盟2023-2024学年高二4月联考数学试题(已下线)北师大版本模块五 专题2 全真基础模拟2(高二期中)(已下线)模块一 专题2 数列的通项公式与求和【讲】(高二下人教B版)(已下线)模块一专题3 数列的实际应用和综合问题单元检测篇A基础卷(高二人教B版)(已下线)模块一 专题4 数列的实际应用和综合问题单元检测篇A基础卷(高二北师大版)(已下线)模块一 专题3 数列的通项公式与求和【讲】(高二下北师大版)
名校
解题方法
6 . 已知数列
中,
为
的前
项和,
.
(1)求数列
的通项公式;
(2)令
,求数列
的前
项和
.
![](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/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08e7d0c282cd14c00ec4e3ff544b2b45.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfbbbe71585920fe16b990ccc129c626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2024-05-04更新
|
1329次组卷
|
4卷引用:第18题 数列不等式变化多端,求和灵活证明方法多(优质好题一题多解)
(已下线)第18题 数列不等式变化多端,求和灵活证明方法多(优质好题一题多解)(已下线)第18题 等差等比综合考查,生成数列通项求和(优质好题一题多解)云南省三新教研联合体高二第二次联考数学试卷和参考答案四川省成都市成都外国语学校2023-2024学年高二下学期4月期中考试数学试题
名校
解题方法
7 . 已知等比数列
的前n项和为
,且
,其中
.
(1)求数列
的通项公式;
(2)在
与
之间插入n个数,使这
个数组成一个公差为
的等差数列,在数列
中是否存在不同三项
,
,
(其中
成等差数列)成等比数列?若存在,求出这样的三项;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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f1c9bdfb252a71b1fc88d7f8082240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
(1)求数列
![](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/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/7955013519718c9ac993531062495e95.png)
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名校
8 . 甲、乙、丙、丁四人练习传球,每次由一人随机传给另外三人中的一人称为一次传球,已知甲首先发球,连续传球
次后,记事件“乙、丙、丁三人均被传到球”的概率为
.
(1)当
时,求球又回到甲手中的概率;
(2)当
时,记乙、丙、丁三人中被传到球的人数为随机变量
,求
的分布列与数学期望;
(3)记
,求证:数列
从第3项起构成等比数列,并求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adfd441e20576bba5c40621dceb6ee29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4290055b7f8e0dc432d011c858b983a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21c72eb6ab46e9f3ffe71cdf050e5666.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
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2024高三·全国·专题练习
解题方法
9 . 已知等差数列
的首项为2,公差为8,在
中每相邻两项之间插入三个数,使得它们与原数列的项一起构成一个新的等差数列
.
(1)求数列
的前
项和
;
(2)若
,
,
,
是从
中抽取的若干项按原来的顺序排列组成的一个等比数列,
,
,令
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2055b891cf3bd623f929ae0e4a5407f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2055b891cf3bd623f929ae0e4a5407f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae8ebcd5b8f8ae04513834a70575816f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e3aaabba90eefb861068bf014f9d0b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b625d02d9054af978b5fb6ec9bee787.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eaa992a449b828df0ff545e233b279b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1efa75d1f118e72d5c8debf97a670841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ed98306783da05c29b0190488f22cfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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名校
解题方法
10 . 已知椭圆
的离心率
.
(1)若椭圆
过点
,求椭圆
的标准方程.
(2)若直线
,
均过点
且互相垂直,直线
交椭圆
于
两点,直线
交椭圆
于
两点,
分别为弦
和
的中点,直线
与
轴交于点
,设
.
(ⅰ)求
;
(ⅱ)记
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075ba8c6fb5ef7288cd3fed425c8e69e.png)
(1)若椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f21c7162941d2b54ebafb1795599195.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/025585172ef67db7ef6af11dd1057ac5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b63fcc8e707d24da005ada77786d5ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/516660cf7bfb7af7a2733ed2e96c4952.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9297e289a9ef977009186083ec738ac.png)
(ⅱ)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3578c86895b9f1c4640a865be22a526.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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2024-04-30更新
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1686次组卷
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6卷引用:7.2 椭圆(高考真题素材之十年高考)
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