1 . 已知数列
满足
,
,
表示不超过
的最大整数(如
,记
,数列
的前
项和为
).
①若数列
是公差为1的等差数列,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e029f140d2209d360a666232e583b4e6.png)
__________ ;
②若数列
是公比为
的等比数列,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7978d7bd6f6caf9ac9837ffce5f89654.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b64049b3dbee60670cd4145ddc82638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b6d151d3f864bae873987f6db9327a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b467b0667aad83b30ce6ef93ed88289.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98a2e0730e197359e0ff1b930c1c4546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2d8811ce6cddf86019c5c84781ad0a6.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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
①若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e029f140d2209d360a666232e583b4e6.png)
②若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b00f4eb7f1bd2ccefbabf0c1dfa8f69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7978d7bd6f6caf9ac9837ffce5f89654.png)
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2017-11-16更新
|
2021次组卷
|
3卷引用:北京市大兴区2017届高三第一次综合练习数学理科试题
2 . 已知数列{an}的各项均为正数,记数列{an}的前n项和为Sn,数列{an2}的前n项和为Tn,且3Tn=Sn2+2Sn,n∈N*.
(Ⅰ)求a1的值;
(Ⅱ)求数列{an}的通项公式;
(Ⅲ)若k,t∈N*,且S1,Sk-S1,St-Sk成等比数列,求k和t的值.
(Ⅰ)求a1的值;
(Ⅱ)求数列{an}的通项公式;
(Ⅲ)若k,t∈N*,且S1,Sk-S1,St-Sk成等比数列,求k和t的值.
您最近一年使用:0次
2017-10-07更新
|
1797次组卷
|
5卷引用:江苏省南京市2018届高三上学期期初学情调研考试数学试题
江苏省南京市2018届高三上学期期初学情调研考试数学试题江苏省南京市2018届高三数学上学期期初学情调研考试数学试题(已下线)专题13 等差、等比数列的应用-《巅峰冲刺2020年高考之二轮专项提升》(江苏)(已下线)专题6.5 数列的综合问题(练)-江苏版《2020年高考一轮复习讲练测》(已下线)专题10 数列通项公式的求法 微点1 观察法(不完全归纳法)、公式法
3 . 已知两个无穷数列
和
的前
项和分别为
,
,
,
,对任意的
,都有
.
(1)求数列
的通项公式;
(2)若
为等差数列,对任意的
,都有
.证明:
;
(3)若
为等比数列,
,
,求满足
的
值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee4464b3b4eb6e52ee02f095aae84f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b708c8dcb2d66eb2ce0b3718a9cd924a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb26cd1601fe7e76e1e2dc0b4909324a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/381576e698a46df8c497e6b5f8346ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/590d6a26e0dabbd16abb6ec968466af7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8c29b297e3ec337c3139c2a1ebed1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e7bec94f0d60f6d65c40c8a01e70b0d.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee4464b3b4eb6e52ee02f095aae84f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8c29b297e3ec337c3139c2a1ebed1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/773aef47607d9a5fdeb5174c0e94c77d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b8896da0a5886c37fbd55d52e81ea61.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee4464b3b4eb6e52ee02f095aae84f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a00682d1dd7f5ed5b11b7fce8677f475.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d31e7a79ba4690f53eae9f9fc7d2be39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c304686d2c8a286fc1d6371a2a2f66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e77a4c414c33b70416c98375aade8f7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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真题
名校
4 . 若无穷数列
满足:只要
,必有
,则称
具有性质
.
(1)若
具有性质
,且
,
,求
;
(2)若无穷数列
是等差数列,无穷数列
是公比为正数的等比数列,
,
,
判断
是否具有性质
,并说明理由;
(3)设
是无穷数列,已知
.求证:“对任意
都具有性质
”的充要条件为“
是常数列”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e7146186b3a33ea5cbff137f9e3437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c0b488096f27c73fc960e27f3b864a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73bc889cb3a977841028e444d62a4d09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e690b25af1cd3e04b784a9f26be3e90e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(2)若无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89d1f32c1605cfdb8e8855051b9f6ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c522c1c881528ab6f9708f6bdd4c4db5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1e52d55280e664b707f4e9ef4cb1554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/928be44c53a39c116c715ab72f2f2d95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cb2db37e079b735acc41ea3035139e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89d1f32c1605cfdb8e8855051b9f6ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d8df5703574ef08007f1eea3cea18e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4611e6b3af6a0f44f9d7a481f0e50d72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89d1f32c1605cfdb8e8855051b9f6ec.png)
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2016-12-04更新
|
1007次组卷
|
16卷引用:上海市复旦大学附属中学2019届高三高考4月模拟试卷数学试题
上海市复旦大学附属中学2019届高三高考4月模拟试卷数学试题2016年全国普通高等学校招生统一考试理科数学(上海卷精编版)北京市西城区北师大实验2017届高三上12月月考数学(理)试题北京西城北师大实验2017届高三上12月月考数学(理)试题(已下线)《2018届优等生百日闯关系列》【江苏版】专题二 第五关 以子数列或生成数列为背景的解答题江苏省南通市海安高级中学2019-2020学年高三上学期9月月考数学试题(已下线)专题14 数列综合-五年(2016-2020)高考数学(文)真题分项(已下线)专题14 数列综合-五年(2016-2020)高考数学(理)真题分项(已下线)考点20 数列的综合运用-2021年高考数学三年真题与两年模拟考点分类解读(新高考地区专用)(已下线)2016年全国普通高等学校招生统一考试理科数学(上海卷参考版)2020年江苏省南通海安市高三学年初学业质量检测数学试题北京市第八中学2021-2022学年高二下学期期中考试数学试题(已下线)重组卷03北京市中关村中学2022-2023学年高二下学期期中调研数学试题(已下线)专题21 数列解答题(理科)-2辽宁省沈阳市东北育才学校科学高中部2023-2024学年高二下学期期中考试数学试题
名校
解题方法
5 . 已知λ,μ为常数,且为正整数,λ≠1,无穷数列{an}的各项均为正整数,其前n项和为Sn,对任意的正整数n,Sn=λan﹣μ.记数列{an}中任意两不同项的和构成的集合为A.
(1)证明:无穷数列{an}为等比数列,并求λ的值;
(2)若2015∈A,求μ的值;
(3)对任意的n∈N*,记集合Bn={x|3μ•2n﹣1<x<3μ•2n,x∈A}中元素的个数为bn,求数列{bn}的通项公式.
(1)证明:无穷数列{an}为等比数列,并求λ的值;
(2)若2015∈A,求μ的值;
(3)对任意的n∈N*,记集合Bn={x|3μ•2n﹣1<x<3μ•2n,x∈A}中元素的个数为bn,求数列{bn}的通项公式.
您最近一年使用:0次
2016-12-04更新
|
638次组卷
|
2卷引用:2020届江苏省南通市海安高级中学高三下学期期初模拟考试数学试题
名校
6 . 已知二次函数
的图象的顶点坐标为
,且过坐标原点
.数列
的前
项和为
,点
在二次函数
的图象上.
(Ⅰ)求数列
的通项公式;
(Ⅱ)设
,数列
的前
项和为
,若
对
恒成立,求实数
的取值范围;
(Ⅲ)在数列
中是否存在这样一些项:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/756b338721e124048b547d3268a67ea5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edaaab658512ef8356e228879582cf94.png)
,这些项都能够构成以
为首项,
为公比的等比数列
?若存在,写出
关于
的表达式;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5f2932b9863fb218b7a990aa80abfc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.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/b8df5cca91bbd56bd8c68d3a9f87012e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(Ⅰ)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
(Ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc0c5e305fdd6773ca9d5ce1d1fb4368.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89d1f32c1605cfdb8e8855051b9f6ec.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/255afadbbd30a385b4a433f95b27962d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851c8763f6700bccac95949fc0d316f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(Ⅲ)在数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/756b338721e124048b547d3268a67ea5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edaaab658512ef8356e228879582cf94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/756b5423a1ef40732567e3b18098270f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a1cd8452683923f3fcade9034f78a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54e956b81c5f97904f3d7c0843c717cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d55a7d201b7336a2b950c7fb05409bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2016-12-03更新
|
1825次组卷
|
5卷引用:2015届北京市顺义区高三第一次统一练习(一模)理科数学试卷
2015届北京市顺义区高三第一次统一练习(一模)理科数学试卷上海市行知中学2018-2019学年高三上学期期中数学试题江西省南昌八中、南昌二十三中等四校2018-2019学年高一下学期期中联考数学试题(已下线)考向18 数列不等式-备战2022年高考数学一轮复习考点微专题(上海专用)(已下线)专题17 数列探索型、存在型问题的解法 微点1 数列探索型问题的解法
2010·上海·二模
名校
7 . 本题共有3个小题,第1小题满分4分,第2小题满分6分,第3小题满分8分.
从数列
中取出部分项,并将它们按原来的顺序组成一个数列,称之为数列
的一个子数列.
设数列
是一个首项为
、公差为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
的无穷等差数列.
(1)若
,
,
成等比数列,求其公比
.
(2)若
,从数列
中取出第2项、第6项作为一个等比数列的第1项、第2项,试问该数列是否为
的无穷等比子数列,请说明理由.
(3)若
,从数列
中取出第1项、第![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
项(设
)作为一个等比数列的第1项、第2项,试问当且仅当
为何值时,该数列为
的无穷等比子数列,请说明理由.
从数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b60fc6993ed58c125ae54ec70c48c718.png)
(1)若
![](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/9aa8a716a31b0f51b70fdf9bdb257909.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfeed3915a3ecf2d0ae0779745fee624.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1bfe8959ea2129b3c3193a147cad712.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2159c002e87e5d2190bd4d55b76549d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
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