1 . 能说明“设数列
的前
项和
,对于任意的
,若
,则
”为假命题的一个等比数列是__________ .(写出数列的通项公式)
![](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/2771c5f04582c545e0f9afc8a2cb9597.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2798e1dcab1f7f0fe3b8a94b3cd6a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef64850887c5c8cad4d574b0b09307a9.png)
您最近一年使用:0次
2022-12-04更新
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536次组卷
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6卷引用:上海市七宝中学2023-2024学年高二上学期期中数学试题
上海市七宝中学2023-2024学年高二上学期期中数学试题北京市十一学校2023届高三上学期12月月考数学试题重庆市十八中两江实验中学校2023届高三上学期第一次全真模拟数学试题(已下线)高考新题型-数列(已下线)北京市西城区2022届高三二模数学试题变式题11-15(已下线)2023年高三数学押题密卷三
名校
解题方法
2 . 若数列
和
满足
,
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e10047d0eafaa4b82525cad54daf8a7c.png)
______ .
![](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/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87ea014220aa658c8baa6e1f43e686a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24269235ef0258890212622634236412.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7ea08b82e405ea38e9fd9a1435fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e10047d0eafaa4b82525cad54daf8a7c.png)
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2022-11-26更新
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885次组卷
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5卷引用:上海师范大学附属中学2022-2023学年高二上学期期中数学试题
上海师范大学附属中学2022-2023学年高二上学期期中数学试题吉林省辽源市第五中学校2022-2023学年高二上学期11月月考数学试题第四章 数列(B卷·能力提升练)-【单元测试】2022-2023学年高二数学分层训练AB卷(人教A版2019)(已下线)第四章 数列(A卷·知识通关练) (1)(已下线)4.3.1 等比数列的概念(第1课时)(分层作业)-【上好课】2022-2023学年高二数学同步备课系列(人教A版2019选择性必修第二册)
名校
解题方法
3 . 已知等差数列
公差为
,前n项和为
.
(1)若
,
,求
的通项公式;
(2)若
,
、
、
成等比数列,且存在正整数p、
,使得
与
均为整数,求
的值;
(3)若
,证明对任意的等差数列
,不等式
恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90bfe21c96489cb30c544d49ddb4c1c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe7bdaaf8b0adf10bf2ef6c1255b1dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1dfe5b322577f02fd19caab8cf20170.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eca7e7b23fd74e3cf89ac541cb7a5d88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd11b72e7bbee52ec744dbd16e89c766.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36662538d838cca2dd082564d6fc6936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c8f6ee1bd20c1b7b4309163e39cc78f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2baa149e5adae5c5085a875a5cd106d.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/362bfce584209628bc4ad3f23e3d7b11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b27971d12f58af42ad7b226b40545b5.png)
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2022-11-26更新
|
508次组卷
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6卷引用:上海市曹杨第二中学2022-2023学年高二上学期期中数学试题
上海市曹杨第二中学2022-2023学年高二上学期期中数学试题(已下线)高二下期中真题精选(压轴40题专练)-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)上海市华东政法大学附属松江高级中学2023-2024学年高二上学期期中考试数学试卷(已下线)期中真题必刷压轴50题专练-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(沪教版2020必修第三册)(已下线)专题7 等比数列的性质 微点1 等比数列项的性质(已下线)专题4.3 等比数列(5个考点八大题型)(2)
名校
解题方法
4 . 在数列
中.
,
是其前n项和,当
时,恒有
、
、
成等比数列,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
___________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abde9618774c7e9ba7cacb092cbb5b33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91621eda36b6084ff545cc844f65c352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
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2022-11-23更新
|
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5卷引用:上海市南洋模范中学2023届高三上学期期中数学试题
5 . 已知数列{an},{bn}满足a1=b1=1,对任何正整数n均有an+1=an+bn+
,bn+1=an+bn﹣
,设
,记Tn=
,则
=____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee1042228389bde772a9deb377a475ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee1042228389bde772a9deb377a475ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686fe64e23291e5fb3ce12fe42cb1d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5249095e0c2a28875a40a5d9c2c56bac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6945610bbce44b73e5199fc8746d5838.png)
您最近一年使用:0次
名校
解题方法
6 . 正项等比数列
中,存在两项
使得
,且
,则
最小值____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2320fcc6aaa1d36b49f8e03b376b80e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa45f845bc583ac93363ae117d591fa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6bec84ea6877e48e01453fcac9c055e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd93ee03569849295ebde055410d1b84.png)
您最近一年使用:0次
2022-11-11更新
|
579次组卷
|
3卷引用:上海市行知中学2023届高三上学期期中数学试题
名校
解题方法
7 . 已知数列
的前
项和为
,满足:
.
(1)求证:数列
为等差数列;
(2)若
,数列
满足
,记
为
的前
项和,求证:
;
(3)在(2)的前提下,记
,数列
的前
项和为
,若不等式
对一切
恒成立,求
的取值范围.
![](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/70214575b0025f5a4d1c19dd1e53fa2d.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2693734765399876e9e93cdb110231c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d00c93d9208f088a049185f55cb70e6.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/f3a868ca08b79f3416de960cbf1016bd.png)
(3)在(2)的前提下,记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c532369aa664a3990e11764a86f1192.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4af909316dd1e25de9370585db21eaa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f49354f6dcc4858d4f56e65ce410a0f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2022-11-11更新
|
1124次组卷
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4卷引用:上海市进才中学2023届高三上学期期中数学试题
上海市进才中学2023届高三上学期期中数学试题(已下线)高二下期中真题精选(压轴40题专练)-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)(已下线)期中真题必刷压轴50题专练-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(沪教版2020必修第三册)天津市2023届高三高考前最后一卷数学试题
名校
8 . 已知数列
的各项均为正数,其前n项和为
,满足
,给出下列四个结论:
①
的第2项小于3;②
为等比数列;③
为递减数列;④
中存在小于
的项
其中正确结论的个数是( )
![](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/4acd06a152df655c118e0e5bb6f1c723.png)
①
![](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/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bfdaa01ae7652656f1f0ccad1a2149c.png)
其中正确结论的个数是( )
A.1 | B.2 | C.3 | D.4 |
您最近一年使用:0次
2022-11-03更新
|
1227次组卷
|
9卷引用:上海市复兴高级中学2023届高三上学期期中数学试题
上海市复兴高级中学2023届高三上学期期中数学试题(已下线)高二下期中真题精选(压轴40题专练)-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)(已下线)期中真题必刷压轴50题专练-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(沪教版2020必修第三册)上海市杨浦高级中学2023届高三下学期开学考试数学试题上海市进才中学2023届高三下学期3月月考数学试题上海市晋元高级中学2023-2024学年高二上学期10月月考数学试题(已下线)专题17 数列(练习)-2(已下线)模块二 数列 不等式-3(已下线)数学(北京卷03)
名校
解题方法
9 . 等比数列
中的项
,
是函数
的极值点,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28ef6f1b2279af482557a8ea46f2e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66b71d11af7b1a235fd976c982a1d23f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a44228c5c2ba14a69648678878fa452c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53af5a710075380bcd807ea491edb156.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ab8770cdae8c48c4e141e79c69573f.png)
A.3 | B.![]() | C.![]() | D.![]() |
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2022-10-22更新
|
627次组卷
|
4卷引用:上海市格致中学2023届高三上学期期中数学试题
名校
10 . 已知等比数列
中,
,则
的公比为__ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07404ab51f404f9411f79bd4f1fde654.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f950990839c7a52ff592ffcc51966fe1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07404ab51f404f9411f79bd4f1fde654.png)
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2023-02-27更新
|
657次组卷
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3卷引用:上海市行知中学2023-2024学年高一下学期期中数学试题