1 . 已知数列
共有
项,且
,若满足
,则称
为“约束数列”.记“约束数列”
的所有项的和为
.
(1)当
时,写出所有满足
的“约束数列”;
(2)当
时,设
“约束数列”
为等差数列.请判断
是
的什么条件,并说明理由;
(3)当
时,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2ea5126ca30d68cc8b70f03860ba2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cf1336dd233a8630e7266f0a83dea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b2ef4791e2c7b4c39194e4a4ce098f.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/b1752474698cd5466dd180df0a00ba9c.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c7a1d739890a8951586e23b78b035bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b15324287c0c631960345a3268b9f1a.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d973faacf520a9af8e193979a6e3b8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e07e175fd880e7ba92c300ede3cdc570.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6ee986f3e8addc977c78f5f82e8f18c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c9ec8f698aefd97055d6dc32a5f13e1.png)
您最近一年使用:0次
2 . 已知数列
,则数列
前9项的下四分位数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ec7510dc49bea69b5961573297f1289.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
A.1 | B.![]() | C.0 | D.![]() |
您最近一年使用:0次
3 . 已知无穷数列
是首项为1,各项均为正整数的递增数列,集合
,若对于集合
中的元素
,数列
中存在不相同的项
,使得
,则称数列
具有性质
,记集合
数列
具有性质
.
(1)若数列
的通项公式为
,判断数列
是否具有性质
,若具有,写出集合
与集合
;
(2)已知数列
具有性质
且集合
中的最小元素为
.集合
中的最小元素为
,当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77b1f76afde7e8136dde47433ea74bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82079a5446d448fb1bea730b968d7e02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9652602f1d23494c53743efe03db6bdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aceba302deb7b46d2058ede7f356f72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0380d25c8bccf9b2abdb668fb1bc5400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f603312b00ec0115ae36344b52ca689b.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c689cdf9d348002587f42b2c26be55f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aceba302deb7b46d2058ede7f356f72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aceba302deb7b46d2058ede7f356f72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/682cbe4cd0d5cf5beb79d3ab89a117f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/997ba7c3da0821973b7f44d2ca07fcd1.png)
您最近一年使用:0次
4 . 对于数列
,规定
为数列
的一阶差分,其中
,规定
为数列
的阶
差分,其中
.若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e041b6f4afd9b5090e4a6b05c9b82ebb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6558223c3276e691c569a665b9ac5d08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f781d8e7a2965dff564da860e2f8d32b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7526cb1a1beabec0268efd30460e19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a014ca4091d08010500b32c882bdf43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffec0d720402ffdfa26f62ed4d6a8ac6.png)
A.7 | B.9 | C.11 | D.13 |
您最近一年使用:0次
解题方法
5 . 已知正项数列
的前n项和为
,且
,数列
的前n项积为
且
,下列说法错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae15ab703c394d3b4605fbcf34a40fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c75329ba7d9388763f4772b880f4b388.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2024-04-22更新
|
588次组卷
|
3卷引用:陕西省汉中市2023-2024学年高三下学期教学质量第二次检测理科数学试卷
陕西省汉中市2023-2024学年高三下学期教学质量第二次检测理科数学试卷陕西省汉中市2023-2024学年高三下学期教学质量第二次检测文科数学试卷(已下线)模块五 专题6 全真拔高模拟6(人教B版高二期中研习)
名校
解题方法
6 . 已知
是各项都为正数的等比数列,数列
满足:
,且
,
.
(1)求数列
的通项公式;
(2)若对任意的
都有
,求实数
的取值范围.
![](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/386f38bdb5b15469034848c67115cbd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46460977b798f237b452f363b9d523e6.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
(2)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9107142dd7cf0c00ccaa15d9c0da2b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
名校
7 . 已知数列
为有穷数列,且
,若数列
满足如下两个性质,则称数列
为m的k增数列:①
;②对于
,使得
的正整数对
有k个.
(1)写出所有4的1增数列;
(2)当
时,若存在m的6增数列,求m的最小值;
(3)若存在100的k增数列,求k的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52c1ee4d7c3f69fdd5a250ab8862d114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9db29473c5e28422317559df73a1037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937c09d82c480e4d67f8a48d3f66c5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/431acf301f0cf1e414b532de94708474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa768d0bb9bcf827b3e7310e35ef0fbf.png)
(1)写出所有4的1增数列;
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45cf86650443d1b86c79b1e3edc7e5c.png)
(3)若存在100的k增数列,求k的最大值.
您最近一年使用:0次
2024-03-27更新
|
1184次组卷
|
4卷引用:河南省郑州市2024届高三第二次质量预测数学试题
8 . 如图,射线
在第一象限,且与x轴正半轴的夹角为
,过点
作
于点A,作线段
的垂直平分线
交x轴于点E,交
于点B,作射线
,以
为边在
的外侧作正方形
,延长
交射线
于点
,以
为边在
的外侧作正方形
,延长
交射线
于点
,以
为边在
的外侧作正方形
……按此规律进行下去,则正方形
的周长为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b12d69150197ca89bac4a76851eaf0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b76d76d91b21a5be2bb58446c7104bc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/062f62f8e6962504213178df9186b70b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b7dc2fe5d920e74d0941b8c1db9ec04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/551d9dbea6e2147f1a626e58ce6e871c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d3cd866636143a514b95de563e43833.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc34876d748f30fa4fc2eb6a686b5ff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35d098990cc285dce3b41e9f7d26275b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52e90dc669b9929e5857a5bba95d6ce1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15ba42cd8dff520c1da49d754e77cc09.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/27/f3512b2e-c6f9-44bb-85b2-99759d8a295a.png?resizew=167)
您最近一年使用:0次
9 .
表示正整数a,b的最大公约数,若
,且
,
,则将k的最大值记为
,例如:
,
.
(1)求
,
,
;
(2)已知
时,
.
(i)求
;
(ii)设
,数列
的前n项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6294a700967de01e6877d686a0e2e79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4160299bf93e7827b97bc5cbb224958e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4c95177c5f6454d2de54bb7b0c182ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae4b8114fcc770a8512cf03da137ca4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9edd29e22f6a7f4d14d9f8d2684d47e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5491950d23d0f3833de05cc3892cacd.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64a7f848e0002222e3fe290e50301e3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ccc57e5668f2a2c1cbc078a767b6855.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16edf0bda2c47ed55f471a1838cd03dc.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/853030075597faf459bec65cd5e0b910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b8178596507fe45cea77096a53d6395.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ce2bf4a86671ab5cefa4d523d8a0fa2.png)
(ii)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beafadba27d9c078bae7761a2b383803.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/47b61920582cc3edd43e273e0cbfa1d4.png)
您最近一年使用:0次
2024-03-26更新
|
1819次组卷
|
8卷引用:福建省泉州市2024届高三质量监测(三)数学试题
福建省泉州市2024届高三质量监测(三)数学试题(已下线)压轴题05数列压轴题15题型汇总-3重庆市第十一中学校2023-2024学年高三第九次质量检测数学试题广东省佛山市顺德区第一中学西南学校2023-2024学年高二下学期第一次月考数学试卷四川省成都市实验外国语学校2023-2024学年高二下学期第一次阶段考试数学试题辽宁省重点高中沈阳市郊联体2023-2024学年高二下学期4月月考数学试卷(已下线)模块五 专题3 全真能力模拟3(人教B版高二期中研习)(已下线)模块四专题6重组综合练(四川)(8+3+3+5模式)(北师大版高二)
名校
10 . 数列
的通项公式为
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f738fe91a4e82dcfe0ec5fdec0e57fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dbd9ff686703cad03aa383e5fec21.png)
A.![]() | B.![]() | C.5 | D.8 |
您最近一年使用:0次
2024-03-26更新
|
878次组卷
|
3卷引用:辽宁省鞍山市第六中学2024届高三下学期第二次质量检测数学试题卷