1 . 已知数列
满足
,
.给出下列四个结论:
①数列
每一项
都满足
;②数列
的前
项和
;
③数列
每一项都满足
成立;④数列
每一项
都满足
.
其中,所有正确结论的序号是_________________ .
![](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/35becfccb4eee2d53a0c92865ebb9b43.png)
①数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455b8aa38eefb19463a0cc24efe3815.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/94351ce858fa3f3a09cfadc2d23d7253.png)
③数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff1c4afd5d0ae01ea180a2e61fe51cef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56e722481402e29b9713b5e75faac482.png)
其中,所有正确结论的序号是
您最近一年使用:0次
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|
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4卷引用:第4章 数列 单元综合检测(难点)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
(已下线)第4章 数列 单元综合检测(难点)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)北京市东直门中学2024届高三上学期阶段检测(10月月考)数学试题重庆市乌江新高考协作体2024届高三上学期期中数学试题北京市第八中学2023-2024学年高三下学期零模练习数学试题
名校
解题方法
2 . 斐波那契数列又称为黄金分割数列,在现代物理、化学等领域都有应用.斐波那契数列
满足
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6a404164c8d199f60d183a59b3647cc.png)
.给出下列四个结论:
① 存在
,使得
,
,
成等差数列;
② 存在
,使得
,
,
成等比数列;
③ 存在常数
,使得对任意
,都有
,
,
成等差数列;
④ 存在正整数
,且
,使得
.
其中所有正确的个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8323901a49cac29afd7d62864f088077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6a404164c8d199f60d183a59b3647cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc55ec78c02306902c0d3fa67753a3d3.png)
① 存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f29c06a3e9a73e905eb87d71efa201c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681ae1522a36768618f7ddaf74abbb7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c596ae902e6408d14d78580c04267f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3d8af4e2b2c48c73e7897eb3da814c8.png)
② 存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f29c06a3e9a73e905eb87d71efa201c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681ae1522a36768618f7ddaf74abbb7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c596ae902e6408d14d78580c04267f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3d8af4e2b2c48c73e7897eb3da814c8.png)
③ 存在常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b01b782f7f5c3e826fc5de64d0327bff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d2cfb4990ffdcb44908db2b7c6948f9.png)
④ 存在正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71eb0f9d985583ea7b685ebdeca7943c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0844d2b5218031f4a67807468b02653c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a00eb8a57a82e7c87e85c575677e3d26.png)
其中所有正确的个数是( )
A.1个 | B.2个 | C.3个 | D.4个 |
您最近一年使用:0次
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|
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|
4卷引用:第4章 数列(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)
(已下线)第4章 数列(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)上海市进才中学2023-2024学年高三上学期期中考试数学试卷北京市海淀区首都师范大学附属中学2024届高三上学期10月阶段检测数学试题(已下线)【一题多变】斐波那契数列1
解题方法
3 . 已知四棱锥
的底面是边长为2的正方形,
,三棱锥
的体积为
,则四棱锥
的外接球的表面积为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1738e419e260a403f33c3f6c74c6d41d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08a9ec3b527947cad9caa4537e0cb7e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24c14ff9b66f21c05e52dc3c8908c2df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
您最近一年使用:0次
名校
解题方法
4 . 在数列
中,若存在非零整数T,使得
对于任意的正整数m均成立,那么称数列
为周期数列,其中T叫做数列
的周期,若数列
满足
,若
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ad71bbef310726e8799208cdacf358f.png)
,当数列
的周期最小时,该数列的前
项的和为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06a4e38ab612865c10b3f394d76c5d6a.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/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/057a9b73fefcd70bd15bfa880c239f36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a60302649eb940748da818199e55da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ad71bbef310726e8799208cdacf358f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87fea137ed54dc83086c686ef9d29abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e946baf1316ac1f219398ecedadf6cf.png)
A.674 | B.675 | C.1347 | D.1349 |
您最近一年使用:0次
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|
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2卷引用:上海市南洋模范中学2023-2024学年高二上学期开学考数学试题
名校
解题方法
5 . 已知
中,过重心G的直线交边
于P,交边
于Q,设
的面积为
,
的面积为
,
,
.
(1)求
;
(2)求证:
.
(3)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/189953649ef79ba7938c5e18c06f5d21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/434b1931c12fc9992a695bad41252a7a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b9802946e68ae1c7153b4496ee14735.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e7aaba80aaeefc1d254e81cd4512d91.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
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|
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13卷引用:上海市位育中学2020-2021学年高二上学期10月月考数学试题
上海市位育中学2020-2021学年高二上学期10月月考数学试题(已下线)第14讲 向量单元复习(讲义)-【教育机构专用】2021年春季高一数学辅导讲义(沪教版2020必修第二册)沪教版(2020) 必修第二册 高效课堂 册末测试卷(已下线)上海期末真题精选50题(大题压轴版)-2020-2021学年高一数学下册期中期末考试高分直通车(沪教版2020必修第二册)(已下线)第8章 平面向量(章节压轴题专练)-2020-2021学年高一数学下册期中期末考试高分直通车(沪教版2020必修第二册)安徽师范大学附属中学2020-2021学年高一下学期期中数学试题广东省深圳实验学校高中部2020-2021学年高一下学期第一阶段考试(月考)数学试题(已下线)第4课时 课后 向量的数乘运算(已下线)专题03 平面向量中的常用方法 -【重难点突破】2021-2022学年高一数学常考题专练(人教A版2019必修第二册)(已下线)6.2.3向量的数乘运算(精练)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)(已下线)重难点01平面向量的实际应用与新定义(2)(已下线)专题02 解三角形(2)-【常考压轴题】湖南省张家界市桑植县第一中学2023-2024学年高一下学期第一次月考数学试卷
22-23高二下·上海·期中
6 . 已知无穷数列
(
)的前n项和为
,记
,
,…,
中奇数的个数为
.
(1)若
,请写出数列
的前5项;
(2)求证:“
为奇数,
,3,4,
为偶数”是“数列
是严格增数列的充分不必要条件;
(3)若
,
2,3,
,求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d1a511265fdde77ed111876f337458.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64810519cca09d8bad1e5c0720b6f70b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccae0d8c29b807d2844ba1e61633a6e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求证:“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/391621c6a983318f5eb3085ede2cc8a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14be3a67d7ff26e1850b3d5f891b7e9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd7a172e3de92f315198a515eef6ebbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51b1e185d6a0ab350cdc947beeb82040.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d1a511265fdde77ed111876f337458.png)
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22-23高二下·上海·期末
7 . 设满足以下两个条件的有穷数列
为n(
)阶“期待数列”:
①
;
②
.
(1)分别写出一个单调递增的3阶和4阶“期待数列”;
(2)若某
(
)阶“期待数列”是等差数列,求该数列的通项公式;
(3)记n阶“期待数列”的前k项和为
(
),试证:
(i)
;
(ii)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6ec0b97655e6bd7004df04457c493ac.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa0fca4198a6d5c5b76e5e1716dc4e2.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f4830a6ec5e0ffd7074b854b4ecdc19.png)
(1)分别写出一个单调递增的3阶和4阶“期待数列”;
(2)若某
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394aee19f94c2b70fcce1d69b31dc7fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/699dfd96d64e59252e384847629c7a75.png)
(3)记n阶“期待数列”的前k项和为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d0a9523f2084cf17b8656c11ab1d95e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/541e541ef98215381bb9120cd39020ca.png)
(i)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7575a54621b480d9d1e0efa5935d8f47.png)
(ii)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08fbfe923e23263b5ae34ee75bb430ab.png)
您最近一年使用:0次
22-23高二下·上海·期末
8 . 对于任意的
,若数列
同时满足下列两个条件,则称数列
具有“性质m”:
①
;②存在实数M,使得
成立.
(1)数列
、
中,
,判断
、
是否具有“性质m”;
(2)设各项为正数的等比数列
的前n项和为
,且
,
,数列
是否具有“性质m”,若具有,请证明你的猜想,并指出M的范围;若不具有,理由?
(3)若数列
的通项公式
.对于任意的
(
),数列
具有“性质m”,且对满足条件的M的最小值
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a70b95c53fb6655721e2a8c61f5c2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc75a9da38151496ca2adce84a977b96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5612ce06759d0f77ca029d10083f7d1e.png)
(1)数列
![](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/ef91b91fc7ac183837bd7c6799f19c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设各项为正数的等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12baad2468950ea89781e38432d88f01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ab4706be6b3854b9c30ab609e5da68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9050ccff2f6fea858342b0fb290ad7bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a70b95c53fb6655721e2a8c61f5c2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8191d51029a192d504bf1b736029f82e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66884efff7400f92b530d69d029778d.png)
您最近一年使用:0次
名校
解题方法
9 . 已知三棱锥
的顶点都在球
的球面上,
平面
,若球
的体积为
,则该三棱锥的体积的最大值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fff504e9c87fdf36221311c45d7bb67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee9c176877b59cd7c34fcc0838b05493.png)
A.![]() | B.5 | C.![]() | D.![]() |
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2023-08-12更新
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10卷引用:上海市嘉定区第一中学2023-2024学年高二上学期期中数学试题
上海市嘉定区第一中学2023-2024学年高二上学期期中数学试题(已下线)第11章 简单几何体(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020必修第三册)广东省韶关市新丰县第一中学2022-2023学年高二下学期期中数学试题四川省绵阳南山中学2023-2024学年高二上学期开学考试数学试题(已下线)广西壮族自治区“贵百河”2023-2024学年高二上学期新高考10月月考测试数学试题(已下线)专题突破卷18 外接球和内切球四川省宜宾市第四中学校2023-2024学年高三上学期10月月考数学(理)试题四川省宜宾市第四中学校2023-2024学年高三上学期10月月考数学(文)试题吉林省辽源市田家炳高中友好学校2024届高三上学期第七十六届期末联考数学试题广东省湛江市第二十一中学2023-2024学年高一下学期期中考试数学试卷
10 . 定义高阶等差数列:对于一个给定的数列
,令
,则数列
称为数列
的一阶差数列,再令
,则数列
是数列
的二阶差数列.已知数列
为2,5,11,21,36,
,且它的二阶差数列是等差数列,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5653b60d16ec4e653518f0562680250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/703cdc7668aa4dcab77e448249f9446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621604766ddd141c86e37da5e71aef26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218cd20fd025841d9b878617d864f71b.png)
A.45 | B.85 | C.121 | D.166 |
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