解题方法
1 . 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)
您最近一年使用:0次
2 . 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:浙江省平阳县浙鳌高级中学2021届高三上学期期初教学质量监测数学试题
名校
解题方法
3 . 设等比数列
,
,
,
的公比为
,等差数列
,
,
,
的公差为
,且
,
.记
.
(1)求证:数列
,
,
不是等差数列;
(2)设
,
.若数列
,
,
是等比数列,求
关于
的函数关系式及其定义域;
(3)数列
,
,
,
能否为等比数列?并说明理由.
![](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/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57483e04fd1840c87ac5325157149877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a548938d87c80ac47910607d3857007f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45482d31d1d7448c9f3922b4d2a55331.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/812be9806122241c476ba1db516c4823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f84b434b39b4689e34b27b7d560077ce.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7936359df4c926b72b48c6fdae55f12d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b76f79be89b8c6227b68eded6b675546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db84454f051d418a4904fa423ab8b304.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d9b6c86435e0ceff94d8ad1cd03737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7936359df4c926b72b48c6fdae55f12d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b76f79be89b8c6227b68eded6b675546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db84454f051d418a4904fa423ab8b304.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
(3)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7936359df4c926b72b48c6fdae55f12d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b76f79be89b8c6227b68eded6b675546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db84454f051d418a4904fa423ab8b304.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6fdd7e9cd5d1764bc5de8add15700ae.png)
您最近一年使用:0次
2020-08-21更新
|
59次组卷
|
5卷引用:江苏省南通、徐州、扬州等六市2018届高三第二次调研(二模)测试数学(文理)试题
江苏省南通、徐州、扬州等六市2018届高三第二次调研(二模)测试数学(文理)试题江苏省苏北六市2018届高三第二次调研测试数学(文科)试题(已下线)专题20 与数列有关的恒成立问题-2018年高考数学(理)母题题源系列(江苏专版)(已下线)专题6.5 高考解答题热点题型---数列的综合应用-2021年高考数学(理)一轮复习-题型全归纳与高效训练突破江西省抚州市东乡区实验中学2022-2023学年高二下学期期中数学试题
解题方法
4 . 在
中,
,角
与角
的平分线长分别为
,
,若
,
的等比中项是
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4c832ae393fc4608d4ab446a065263d.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8f88798ec42a58dccd212586382b23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f149e83812e72efd7dd3dfc78d0134ae.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/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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46947da34351a77f846092424cf7bb39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4c832ae393fc4608d4ab446a065263d.png)
您最近一年使用:0次
名校
解题方法
5 . 已知正项数列
的前n项和为
,且
是4和
的等比中项,数列
,其前n项的和为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbfc875ca919921e8f63a6fca648561b.png)
__________ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a8462c07c0143853c1bec52084360e.png)
__________ .
![](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/23016d1186ebefd8d67387f43f100229.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e722d1cb06e597485399a64c75b14a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbfc875ca919921e8f63a6fca648561b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a8462c07c0143853c1bec52084360e.png)
您最近一年使用:0次
2020-07-20更新
|
638次组卷
|
2卷引用:四川省遂宁市船山区第二中学校2020届高三高考适应(二)考试数学(文)试卷
解题方法
6 . 设等差数列
的前n项和为
,
.
(1)求
及
;
(2)设
,数列
的前n项和为
,是否存在正整数
,使得
,
成等比数列?若存在,求出所有满足条件的
;否则,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/decc158d90a1359ea4bd557c865bdcf7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.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/f3b70aeff7c01e637f9caac346798ff8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d703eb7edee7f4aa351f70bd2584d0b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e4423e494000eacecc198bcb8f19cf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
您最近一年使用:0次
2020-07-16更新
|
362次组卷
|
2卷引用:重庆市2019-2020学年高一下学期期末联合检测数学试题
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 . 已知数列
的前
项和为
,且
,数列
是公差为0的等差数列,且满足
,
是
和
的等比数列.
(1)求数列
和
的通项公式;
(2)求
;
(3)设数列
的通项公式![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c906a59ac5cd05f4d5ac2d6a4fe5aab3.png)
,求
;
![](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/361396636c3472bf431c9ca83d4c493e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/481eb188d30b1553f2fc5b9150bbc841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f6714682274c31a328bf796e235900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/881b37f60005f7f8665a096a74a2ab6f.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e634c8c96a14fecd9734472edf50bde.png)
(3)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c906a59ac5cd05f4d5ac2d6a4fe5aab3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fe2e15ba11f38188ba4445117d0914f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee121a0bd2acbcf3a1aeb6ee22926655.png)
您最近一年使用:0次
9 . 设首项为a1的正项数列{an}的前n项和为Sn,q为非零常数,已知对任意正整数n,m,Sn+m=Sm+qmSn总成立.
(1)求证:数列{an}是等比数列;
(2)若不等的正整数m,k,h成等差数列,试比较amm•ahh与ak2k的大小;
(3)若不等的正整数m,k,h成等比数列,试比较
与
的大小.
(1)求证:数列{an}是等比数列;
(2)若不等的正整数m,k,h成等差数列,试比较amm•ahh与ak2k的大小;
(3)若不等的正整数m,k,h成等比数列,试比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/732a5ba0cbd7c191ecfdf841f2817d5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d77cbe256d197e83826113805d1fdc2.png)
您最近一年使用:0次
解题方法
10 . 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 |
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2020-05-21更新
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911次组卷
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6卷引用:2020届上海市虹口区高三下学期二模数学试题
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