20-21高三下·全国·阶段练习
名校
解题方法
1 . 已知公差不为零的等差数列
的前
项和为
,且满足
,
,
成等比数列,
,数列
满足
,前
项和为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b1cc8fdd212e13671a103eebf2c1608.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/08eb71ecf8d733b6932f4680874dbbf3.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/f65fc200f10b97588a0c9896277c9c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d1888ff3d98e22154c081dd37a54fbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2062a1f5bc5de088d1dd48cd6a941368.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/4b1cc8fdd212e13671a103eebf2c1608.png)
您最近一年使用:0次
2021-03-23更新
|
527次组卷
|
4卷引用:天一大联考2021届高三下学期阶段检测(四)理科数学试题
(已下线)天一大联考2021届高三下学期阶段检测(四)理科数学试题河南省十所名校2020-2021学年高中毕业班阶段性测试数学理科(四)试题江西省吉安市遂川中学2021届高三下学期阶段性测试(四)数学(理)试题(已下线)专题03 《数列》中的压轴题-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册)
2 . 已知等比数列
的前n项和为
,且
.
(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3项
,
,
,(其中m,k,p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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33499e9bca358d0dc60b07d72e86e5a6.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)
您最近一年使用:0次
2021-02-07更新
|
1712次组卷
|
7卷引用:人教A版(2019) 选择性必修第二册 新高考名师导学 第四章 复习参考题4
解题方法
3 . 在正项等差数列
和正项等比数列
中,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
A.若![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
名校
解题方法
4 . 已知
是公差不等于0的等差数列,
是等比数列
,且
.
(1)若
,比较
与
的大小关系;
(2)若
.
①判断
是否为数列
中的某一项,并请说明理由;
②若
是数列
中的某一项,写出正整数m的集合(不必说明理由).
![](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/c9fc82353331abee0828dee9b38c08f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bd1721c727549b699f39a02cc2aa2d3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/494a1444abd3f9441b30d999f65b3203.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b400065fbaf8e7fbc286fe770608700d.png)
①判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac648580405ecaa29e91d45738a08af7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f64696f60c533ad95dc7890eb902741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
2020-11-15更新
|
255次组卷
|
2卷引用:北京师大二附中2022届高三10月月考数学试题
解题方法
5 . 若数列
满足:存在实数
,使得
对任意
、
都成立,则称数列
为“
倍等阶差数列”.已知数列
为“
倍等阶差数列”.
(1)若
,
,
,求实数
的值;
(2)在(1)的条件下,设
.
①求数列
的通项公式;
②设数列
的前
项和为
,是否存在正整数
、
,且
,使得
、
、
成等比数列?若存在,求出
、
的值,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f886755029b84ea509e93eaf8bbc17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bae03ee4ac75dacfb026290e4207dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9dae8e6c9b93458f324f30538a3eb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fa69dde104dcf963e67647e801e0149.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(2)在(1)的条件下,设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5674b7bb417ca0697c719f608ec669a0.png)
①求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
②设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5da72309d2507e2f5e5ed88d8cc08963.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/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c5bbf2770cc61ba381e4a5ee5e1a26c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0833aa85a3389c7fc576b5f55359100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6996aacf881b439908670c81a749ddd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
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6 . 已知椭圆
,过左焦点
的动直线交椭圆于
,
两点,
为直线
上一定点(不是与
轴的交点),直线
,
,
的斜率分别为
,
,
.
(1)判断
,
,
是否恒为等差数列,若是,给出证明;若不是,请说明理由;
(2)对任意给定的点
,是否都存在一条过点
的直线
,使得
,
,
为等比数列?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4129f43a6af21631251511e63e2ac4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/051be09b4e835cf68f624541a843018d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf434334b09cc0fdd4e86e84e6ceb00.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf434334b09cc0fdd4e86e84e6ceb00.png)
(2)对任意给定的点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf434334b09cc0fdd4e86e84e6ceb00.png)
您最近一年使用:0次
2020-09-14更新
|
360次组卷
|
2卷引用:天津市2021届高三高考模拟数学试题
7 .
是公比不为1的等比数列
的前n项和,
是
和
的等差中项,
是
和
的等比中项,则
的最大值为( )
![](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/05201ef79a5d5904f492845396fb5470.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a48e81b54f78b96294295542b010dfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e9fb008c04818c56dd78fe1f2cc16db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3bf6071c209699ee6bd8e6199164617.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee05c39bbbe3610c7e2b9ea95b5f4afa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
8 . 设等比数列
的前n项和为
,首项
,且
,已知
,若存在正整数
,使得
、
、
成等差数列,则
的最小值为( )
![](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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f25a0462c8213ee2425b02f44c0537b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d9c5e441c34cd0ebaa1c64078a51142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beeacf48580bbafc96926ce1291def0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54ff82eef77f50103ad913084c0794ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1019d4ad2e3fb4a7abb66e0e9e55b556.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab86e6c1601d1f628c6c22488e66e636.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1019d4ad2e3fb4a7abb66e0e9e55b556.png)
A.16 | B.12 | C.8 | D.6 |
您最近一年使用:0次
2020-05-21更新
|
906次组卷
|
6卷引用:湖北省部分重点中学2020-2021学年高三上学期期末联考数学试题
湖北省部分重点中学2020-2021学年高三上学期期末联考数学试题(已下线)预测07 数列-【临门一脚】2021年高考数学三轮冲刺过关(新高考专用)【学科网名师堂】(已下线)专题09 《数列》中的存在性问题-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册)2020届上海市虹口区高三下学期二模数学试题(已下线)山东省日照市2023届高三一模考试数学试题变式题6-10(已下线)专题17 数列探索型、存在型问题的解法 微点2 数列存在型问题的解法
名校
9 . 若△ABC的内角A、B、C所对的边a、b、c成等比数列,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2faef719ca2fc6f4eca081c33f2e5d1c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2020-02-20更新
|
926次组卷
|
4卷引用:期末综合检测03-2020-2021学年高一数学下学期期末专项复习(苏教版2019必修第二册)
(已下线)期末综合检测03-2020-2021学年高一数学下学期期末专项复习(苏教版2019必修第二册)(已下线)专题01 《数列》中的典型题-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册)重庆市第一中学2018-2019学年高一下学期4月月考数学试题重庆市万州第三中学2018-2019学年高一下学期期中数学试题
19-20高二上·北京西城·期中
名校
10 . 有穷数列
满足
,且
成等比数列. 若
,则满足条件的不同数列
的个数为_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f56b6233ec28b50ec576d1062b7bbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/308bafeb34077dba1139f4a9a496259b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bade2ae00bc3ff7c52ab59c7be36fb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f175e1b1a6afea552a048b65bc73d58e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
您最近一年使用:0次