名校
解题方法
1 . 已知等差数列
的前
项的和为
,且
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3195af2fcb60759ccf57336ed41d928.png)
,则正整数
的值为_________ .
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35319aade43a0deae40f185b74f99e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3195af2fcb60759ccf57336ed41d928.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea23457d29048051cfad1300ee0df2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2 . 已知数列
满足:
,且
,
.
(1)证明:数列
是等比数列,并求数列
的通项公式;
(2)若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b5299d8681e97043a0e449cde0f9731.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be9b1d808f2e220696fba4590677ea0f.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b463e643a730e8f11504f135a1400909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
名校
解题方法
3 . 已知数列
满足
(
为正整数),
,设集合
.有以下两个猜想:①不论
取何值,总有
;②若
,且数列
中恰好存在连续的7项构成等比数列,则
的可能取值有6个.其中( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fab51121848ce166035ceab6f4e00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19270ac238f89bde5aeb61c622c1d68b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9972b9f5d541ff043675df369de82748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35a2410ce34b36954ed4923e600d42f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6225bb97266c814a33b98c1e90e03e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.①正确,②正确 | B.①正确,②错误 | C.①错误,②正确 | D.①错误,②错误 |
您最近一年使用:0次
2024-06-01更新
|
163次组卷
|
4卷引用:上海市格致中学2021-2022学年高二下学期期中数学试题
上海市格致中学2021-2022学年高二下学期期中数学试题(已下线)4.2等比数列及其通项公式(第1课时)(作业)(夯实基础+能力提升)-2022-2023学年高二数学精品教学课件(沪教版2020选择性必修第一册)上海市实验学校2023-2024学年高三下学期四模数学试题 (已下线)【练】专题5 分段数列问题
4 . 在等差数列
中,
,公差为
,前
项和为
,当且仅当
时
取最大值,则
的取值范围_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06dd3c3b45125d4b484e2894992610f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.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/08ec5d76db9bd05547932966c9913dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
您最近一年使用:0次
2024-05-27更新
|
559次组卷
|
27卷引用:上海市华东师范大学第二附属中学2017届高三上学期期中数学试题
(已下线)上海市华东师范大学第二附属中学2017届高三上学期期中数学试题河北省石家庄市第一中学2017-2018学年高一下学期期中考试数学(理)试题河北省石家庄市第一中学2017-2018学年高一下学期期中考试数学(文)试题上海市格致中学2018-2019学年高二上学期第一次月考数学试题上海市吴淞中学2018-2019学年高三上学期10月月考数学试题河南省郑州市八校2020-2021学年高二上学期期中联考数学(文)试题上海市建平中学2023届高三上学期11月月考数学试题上海市洋泾中学2024届高三上学期开学考试数学试题2014年全国普通高等学校招生统一考试文科数学(江西卷)(已下线)2013-2014学年浙江省平阳中学高二下学期期末考试文科数学试卷(已下线)2015届甘肃省兰州第一中学高三12月月考数学试卷2014-2015学年河南省郑州47中高二上学期第一次月考试理科数学卷2015-2016学年陕西省西安市第七十中学高二10月月考理科数学试卷2016-2017学年河南八市重点高中高二文上月考一数学试卷步步高高二数学暑假作业:【理】作业9 等差数列步步高高二数学暑假作业:【文】作业9 等差数列湖南省衡阳市耒阳市第二中学2019-2020学年高二上学期8月月考数学试题(已下线)题型04 等差数列前n项和最大最小问题-2020届秒杀高考数学题型之数列(已下线)专题18 等差数列与等比数列-十年(2011-2020)高考真题数学分项人教A版(2019) 选择性必修第二册 过关斩将 第四章 数列 4.2 等差数列 4.2.2 等差数列的前n项和公式 第2课时 等差数列前n项和的综合运用 基础过关练四川省攀枝花市第十五中学校2021-2022学年高一下学期第一次月考数学试题(已下线)8.1 等差数列河南省漯河市高级中学2023-2024学年高三上学期摸底考试数学试题河南省焦作市博爱县第一中学2023-2024学年高三上学期8月月考数学试题(已下线)考点3 等差列的前n项和及其性质 2024届高考数学考点总动员【练】(已下线)专题05 数列小题(7类题型,文科)(已下线)模块二 类型5 思维漏洞类12个易错高频考点
解题方法
5 . 正项等比数列
中,
与
是
的两个极值点,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/972a067d9d035b9be7768a2e23dee986.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e29f6ffe091d4f51b3b7c8c9ca88005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c74fd9b94d7e7c54207580a3823b381a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/972a067d9d035b9be7768a2e23dee986.png)
您最近一年使用:0次
名校
6 . 设
是公比不为1的无穷等比数列,则“
为严格减数列”是“存在正整数
,当
时,
”的______ 条件.(选填“充分而不必要条件”,“必要而不充分条件”,“充分必要条件”,“既不充分也不必要条件”)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ccd4537f4dee2050ade38b972eb9b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/985dc26a89252b2e8dea815c529a2ffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25809c4ad8f07e80b10fdb5b40d6dfae.png)
您最近一年使用:0次
名校
解题方法
7 . 记等差数列
的前
项和为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b11e2bf8d65c24fc845446a32d881bd4.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/0ac5b045f699a9507ae0cff186029369.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b11e2bf8d65c24fc845446a32d881bd4.png)
您最近一年使用:0次
8 . 数列
中的项按顺序可以排列成如下图的形式,第一行一项,排
;第二行2项,从左到右分别排
,
;第三行3项,…依次类推,设数列
的前
项和为
,则满足
的最小正整数
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.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/6c1ccc6c74b8754e9bcbb3f39a11b6f1.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/38f2c173004bcd025e5d4759fa14faa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
4 | |||
4 | ![]() | ||
4 | ![]() | ![]() | |
4 | ![]() | ![]() | ![]() |
…… |
A.65 | B.66 | C.78 | D.79 |
您最近一年使用:0次
9 . 已知等比数列
的前
项和为
,
,且
成等差数列.
(1)求
;
(2)设
,
是数列
的前
项和,求
;
(3)设
,
是
的前
项的积,求证:
(
为正整数).
![](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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae1fb6143a59cb6c6e4a2c838d98680.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c26222fab28d45935efbeb96dccc9f98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.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/c35926bf4b8e2c163c20942173cffcce.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6582a3657759ff3f6ae698edba3afd52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15520cf5be7c2685975aac51bc99ac4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6dfd8c41024b1f33e2ace6af0c50d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
名校
解题方法
10 . 对于有穷数列
,若存在等差数列
,使得
,则称数列
是一个长为
的“弱等差数列”.
(1)证明:数列
是“弱等差数列”;
(2)设函数
,
在
内的全部极值点按从小到大的顺序排列为
,证明:
是“弱等差数列”;
(3)证明:存在长为2024的“弱等差数列”
,且
是等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce381e1cb026a858d8c7b94e1754844.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43a56a30994f7d7e2f15da593b05a56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0a56586686dfb815fe548957ddcfefb.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1947fd8b1e5fa9096c13256fdb3a23ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7833e32ccdb51745b01fc7877762492.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20655342f9ace8b50a50f5eae6f37beb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20655342f9ace8b50a50f5eae6f37beb.png)
(3)证明:存在长为2024的“弱等差数列”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次