名校
解题方法
1 . 已知数列
中,
,
,
.设
.
(1)证明:数列
是等比数列;
(2)设数列
的前
项的和为
,求
.
(3)设
,设数列
的前
项和
,求证:
.
![](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/9c9b6e51986fe5d7a7265e0e93adcb4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b3fbc9f52077c96e41e952d3cae583c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5653b60d16ec4e653518f0562680250.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设数列
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68e3063fcab5b92188618b4500cb1be4.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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02e80983b88cdf6b540502816c87d13.png)
您最近一年使用:0次
2022-12-03更新
|
738次组卷
|
4卷引用:第4章 数列 (单元重点综合测试)-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 (单元重点综合测试)-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)江苏省宿迁中学2022-2023学年高二上学期期中数学试题(已下线)期末考试押题卷01(考试范围:选择性必修第一册)-2022-2023学年高二数学新教材同步配套教学讲义(苏教版2019选择性必修第一册)(已下线)4.3 等比数列(练习)-高二数学同步精品课堂(苏教版2019选择性必修第一册)
名校
解题方法
2 . 已知数列
的首项
,前
项和为
,数列
满足
,正项数列
满足
.
(1)求数列
的通项公式;
(2)若数列
前
项和为
对任意
恒成立,求实数
的取值范围;
(3)对于大于1的正整数
、
(其中
),若
、
、
三个数经适当排序后能构成等差数列,求符合条件的数组
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d4dc52c2ae6e143721bb434ef0df98f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ff322fc049488a438d8e880b51cfec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f60363d0a8707940b62e5ac4e3ed163a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa122c0d4b14c391c7f612a13ff23f5f.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/749a622e0249b075373103eb31ff50dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45395c29f402da0d60cc4816719d5ee8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/854ccb472313417fbf23ce64a39a1824.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)对于大于1的正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8edfabf4c1120b945b6344f60fab63c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80fc00ee81424906f92879d14cc6356c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/819d8b4711cacd6265f5697d4cc188c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eed56ce9d863bba9b5ea05aebf236b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d472d470925e9f264eda6f9d680e017.png)
您最近一年使用:0次
名校
3 . 已知
,
,则
的最大值等于__________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48bc4e7bd7334c308322b76e7b1d0c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/337a9a3fd11e27e74b014254693768a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
4 . 南宋数学家杨辉所著的《详解九章算法商功》中出现了如图所示的形状,后人称为“三角垛”(下图所示的是一个4层的三角跺)“三角垛”最上层有1个球,第二层有3个球,第三层有6个球,…,设第n层有
个球,从上往下n层球的球的总数为
,则下列正确的是( ).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/38b8b231-fd39-4ee4-accb-3f7939ceface.png?resizew=115)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/38b8b231-fd39-4ee4-accb-3f7939ceface.png?resizew=115)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
22-23高二上·上海·期中
解题方法
5 . 已知点
在直线
上,
为直线l与y轴的交点,等差数列
的公差为1(
).
(1)求数列
,
的通项公式;
(2)设
,求
的值;
(3)若
,且
,求证:数列
为等比数列,并求
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c6437c5e60fb22c44918407eb5c9d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9944bcd0c383c1d3d04c6ab90cacced9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a70b95c53fb6655721e2a8c61f5c2c.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a77b3a20b653e1979a93f119ad40406d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd93dfc99f8df4a7053e7e3a6838394c.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7216b901691e2c6140379588988a479.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea6578afabc23f5d7041b88c3790dd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eda624fa223cc191d35e23f0e6cd148.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
您最近一年使用:0次
6 . 定义:对于任意数列
,假如存在一个常数
使得对任意的正整数
都有
,且
,则称
为数列
的“上渐近值”.已知数列
有
(
为常数,且
),它的前
项和为
,并且满足
,令
,记数列
的“上渐近值”为
,则
的值为 _____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423744758955a28ba23a32c169dbbcbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a50e5a21e33a7b9ea0a84cede39982d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.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/a936a61ab8a3ca7d5c8cb00fd7fd70e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.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/9df945ccc3744817dc13ead49253f5fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2f7d0b329709c40a47a9dee90d86b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/443564053aa217fc84a72c8d8402eaf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b821e5e9e5de011dd1e74a5bee378d7f.png)
您最近一年使用:0次
22-23高二上·浙江·期末
7 . 已知数列
满足
,
.
(1)证明数列
为等比数列,并求
的通项公式;
(2)设
,数列
的前
项和为
,若存在
,使
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac85f2734fc720360f0fc8cecad570b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683df050cafa480b6ed1103b0edad6bc.png)
(1)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c7d94406136605c5bc9cd9295d6c9fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd59ab80163c89dc77b59b376f359cb9.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37259220648a6fcfeed221612ed27704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2022-09-29更新
|
2117次组卷
|
7卷引用:上海市高桥中学2022-2023学年高二上学期期末数学试题
上海市高桥中学2022-2023学年高二上学期期末数学试题(已下线)高中数学 高二上-8河北省衡水市第二中学2022-2023学年高二上学期期中数学试题(已下线)第7讲 数列求和9种常见题型总结 (3)(已下线)拓展三:数列与不等式 -【帮课堂】2022-2023学年高二数学同步精品讲义(人教A版2019选择性必修第二册)(已下线)拓展四:数列大题专项训练(35道) -【帮课堂】2022-2023学年高二数学同步精品讲义(人教A版2019选择性必修第二册)(已下线)专题06 数列在高考中的考法(难点,十一大题型+过关检测专训)-2023-2024学年高二数学《重难点题型·高分突破》(人教A版2019选择性必修第二册)
名校
解题方法
8 . 已知数列
是首项为
,公差为
的等差数列,数列
的前
项的和为
,数列
是公比为
的等比数列.
(1)若
,求数列
的通项公式;
(2)若数列
的前
项和为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.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/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ba07273343c265e60ecae346790fd83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8050391385b496e9c059201e4f12600a.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/6945610bbce44b73e5199fc8746d5838.png)
您最近一年使用:0次
9 . 已知数列
的各项均为正数,且
,对任意的正整数
,都有
.
(1)求证:
是等比数列,并求出
的通项;
(2)设
,若数列
中去掉
的项后,余下的项组成数列
,求
;
(3)在(2)中,设
,数列
的前
项和为
,是否存在正整数
、
且
,使得
、
、
依次成等差数列,若存在,求出
的值;若不存在,请说明理由.
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3998df04d0a8ded946c3f39d545fdc7e.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2de706dc5f0439b989273a5367f63a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98851ec1ca2341b0ba5972b20122a112.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/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94f9717b02a5aeefb76b86cd6911ff2f.png)
(3)在(2)中,设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2739d4e88c3dedb057fee4bd223db7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.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/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667160d99fbb37feca6001a20e4e1cf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1752474698cd5466dd180df0a00ba9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
解题方法
10 . 已知等比数列
为增数列,满足
,前3项和
.
(1)求数列
的通项公式;
(2)令
,求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2693734765399876e9e93cdb110231c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86551283c9dfa1c39bdc9b0dd546803.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c7c5bab8939c2728b1824834e921925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2022-06-29更新
|
489次组卷
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4卷引用:上海市建平中学2021-2022学年高二下学期期末数学试题
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