1 . 中国古代科学家发明了一种三级漏壶记录时间,壶形都为正四棱台,自上而下,三个漏壶的上底宽依次递减1寸(约3.3厘米),下底宽和深度也依次递减1寸.设三个漏壶的侧面与底面所成的锐二面角依次为
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f64fa38725c136504f723019a18dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e93fa313adc4ac7608ba9449fd755212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e8d4017e1a37acb0c8e00508be472b2.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2 . 等差数列
中,设前
项和为
,
,则
等于( )
![](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/5733e47b25c81541ddd18dc39c42904a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba48780e63a87aaf7f1d7fa29dd56b5c.png)
A.80 | B.85 | C.90 | D.95 |
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7日内更新
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382次组卷
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3卷引用:北京市铁路第二中学2023~2024学年高二下学期期中考试数学试卷
北京市铁路第二中学2023~2024学年高二下学期期中考试数学试卷北京市第六十六中学2023-2024学年高二下学期6月月考质量检测数学试题(已下线)高二下期末考前押题卷02--高二期末考点大串讲(人教B版2019选择性必修)
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3 . 已知等比数列
中,
,且
,
,
成等差数列,则数列
公比为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c68c1d8445209858204103448174252a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0462c9dc4a0bd08a0ec1cc07f1d2f3e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35b8538dcc10d54220cea20e48e83884.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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2024-05-02更新
|
286次组卷
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2卷引用: 北京市八一学校2023-2024学年高二下学期期中考试数学试卷
解题方法
4 . 在等差数列
中,已知
,
与
的等差中项为
,等比中项为
,则通项公式![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
________ ;前
项和![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/065be21c20118f713d288f3a84ad114f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
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5 . 正实数构成的集合
,定义
,且
.当集合
中的元素恰有
个数时,称集合A具有性质
.
(1)判断集合
是否具有性质
;
(2)设集合
具有性质
,若
中的所有元素能构成等差数列,求
的值;
(3)若集合A具有性质
,且
中的所有元素能构成等差数列.问:集合A中的元素个数是否存在最大值?若存在,求出该最大值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff9423a8ca3d361e6c2e306e85f645.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dca01ec02f3776fcd41abf91c11f00cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c3aa0dd21599a617660672ea6410c65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636c838e9c10d079e5df897fce90761b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d00b592b51981ec491c1a1275593143.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71f9d1bf24fb71dbec06d9728abde542.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
(2)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04ee39cb5dda61782c6c0989fe5f8016.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6276b807e05eebe754764c1fc29cb5d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd5371a6f0f82c65dd22f75f8b807c1.png)
(3)若集合A具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636c838e9c10d079e5df897fce90761b.png)
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2023-07-10更新
|
290次组卷
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3卷引用:北京市丰台区2022~2023学年高二下学期期末数学试题
名校
解题方法
6 . 已知数列
,设
,若
满足性质
:存在常数
,使得对于任意两两不等的正整数
、
、
,都有
,则称数列
为“梦想数列”.
(1)若
,判断数列
是否为“梦想数列”,并说明理由;
(2)若
,判断数列
是否为“梦想数列”,并说明理由;
(3)判断“梦想数列”
是否为等差数列,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ecc403f4056f29f923279ae5b5ea80c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aad93ac9e7576a829fea4052290d794.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be0f90a1b3bb8d6b26f3755657f086f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b20170468efcb900940b41b40cc3bd7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
(3)判断“梦想数列”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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解题方法
7 . 如果数列
满足不等式
(其中
),我们就称这个数列为“
数列”,对于以下关于“
数列”的四个结论:①等差数列均为“
数列”;②“
数列”一定是递增数列;③“
数列”通项公式可以是
;④“
数列”中对于任意
,都满足
.所有正确结论的序号是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/229a0e453d4c92aaf2c8f77cfbd94314.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/465d1f94e8c4ebaa189f9dc1c22bd944.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0ad7e7853a069537387b5192f73844.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0ad7e7853a069537387b5192f73844.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0ad7e7853a069537387b5192f73844.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0ad7e7853a069537387b5192f73844.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0ad7e7853a069537387b5192f73844.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f258a3239581f00bf1afe37bce06ac3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0ad7e7853a069537387b5192f73844.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b513ec2b07b56d03eae65c3680c26b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b0c21aa20cf1723c14eca005ea48403.png)
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8 . 首项为1的等比数列
中,
,
,
成等差数列,则公比![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad0d99fef1aa4dbcc6dc7b30b7d2c9a9.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a37f1b45e929b42044626edb63681fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b2667a6c91b720ca9b42d092c776cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad0d99fef1aa4dbcc6dc7b30b7d2c9a9.png)
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2023-11-23更新
|
1289次组卷
|
8卷引用:北京市石景山区2023届高三上学期期末数学试题
北京市石景山区2023届高三上学期期末数学试题北京市顺义区第一中学2022-2023学年高二下学期6月月考数学试题北京市汇文中学2023-2024学年高三上学期期中考试数学试题新疆乌鲁木齐市第三十一中学2020-2021学年高一下学期期末考试数学试题河南省体育中学2022-2023学年高二上学期期中数学试题(已下线)考点7 等差、等比数列的联姻 2024届高考数学考点总动员【练】(已下线)模块3 专题3 第2套 小题入门夯实练【高二人教B】上海市闵行中学2023-2024学年高一下学期期末考试数学试卷
9 . 给定数列
,若满足
且
,对于任意的n,
,都有
,则称数列
为“指数型数列”.
Ⅰ
已知数列
,
的通项公式分别为
,
,试判断
,
是不是“指数型数列”;
Ⅱ
若数列
满足:
,
,判断数列
是否为“指数型数列”,若是给出证明,若不是说明理由;
Ⅲ
若数列
是“指数型数列”,且
,证明:数列
中任意三项都不能构成等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4f5d7eb7518d6676fe5a7f56e64d516.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cc2e93cee2e6a921b66d250bd046b33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/613e96d4842008797a0f7071d48ce4e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac67c97e7df5ccb0672b29266cd39eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee4464b3b4eb6e52ee02f095aae84f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1897b6556a77133581546a0b52f0095e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cdccd587b3a184c5315d090918137f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee4464b3b4eb6e52ee02f095aae84f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90fa45d99faf476e983cd7d31a402135.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efe4641b14935ac71265ba4211332f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54aacbbb02e19138e48dd07fca0e0813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b466697b27f8e73efd78431714b064.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
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10 . 数列
是等差数列 ,
是各项均为正数的等比数列,公比
,且
,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eda6dc559d07bc22c9a0ed1e3a6d01d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0426eb784f9c387f6a0d2e7e21a11118.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2019-02-02更新
|
1345次组卷
|
5卷引用:【区级联考】北京市昌平区2019届高三第一学期期末数学(理)试题