名校
1 . 已知
是等差数列,
是公比不为
的等比数列,
,
,
,且
是
与
的等差中项.
(1)求
和
的通项公式.
(2)求![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46e92ff41a3037a51bf594df6f73bc3.png)
(3)若
,证明:
.
(4)数列求和问题的关键是根据通项公式特点找到适合的求和方法,并进行合理变形,观察下列数列通项公式特点,填表:
![](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/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7def23f30138e0b7c4c1e498d6903a6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a8ec38ab7e6912bcc97513a359bd5e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1320e2e9d9c398ec700482b06153d05b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e82778985cd2e9f80ca7b7cabb1a85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9632e7e5a6eb0c85cb44940c60618d67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57483e04fd1840c87ac5325157149877.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46e92ff41a3037a51bf594df6f73bc3.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9169c81b9643e9dcd5c945d580186c97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e06ae105393888c9e02fb2437428217c.png)
(4)数列求和问题的关键是根据通项公式特点找到适合的求和方法,并进行合理变形,观察下列数列通项公式特点,填表:
通项公式 | 求和方法名称 | 变形成可求和形式 |
![]() | ||
![]() | ||
![]() |
您最近一年使用:0次
解题方法
2 . 如图,正方形ABCD的边长为8,取正方形ABCD各边的中点E,F,G,H,作第2个正方形EFGH,然后再取正方形EFGH各边的中点I,J,K,L,作第3个正方形IJKL. 依此方法一直继续下去.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/b47c7337-7604-4634-b54a-082418123151.png?resizew=147)
①从正方形ABCD开始,第7个正方形的边长为___ ;②如果这个作图过程可以一直继续下去,那么作到第n个正方形,这n个正方形的面积之和为___ .
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/b47c7337-7604-4634-b54a-082418123151.png?resizew=147)
①从正方形ABCD开始,第7个正方形的边长为
您最近一年使用:0次
3 . 在等比数列
中,填写下表.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
题号 | ||||
(1) | 3 | |||
(2) | 4 | |||
(3) | 4 | 4 | 256 | |
(4) | 3 | 5 | 48 | |
(5) | 3 | 2 | 24 |
您最近一年使用:0次
2023-10-11更新
|
22次组卷
|
2卷引用:北师大版(2019)选择性必修第二册课本习题第一章3.1 等比数列的概念及其通项公式
23-24高二上·全国·课后作业
4 . 已知数列
是公比为
的等比数列,试根据所给条件填写下表:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
题号 | ![]() | ![]() | ![]() | ![]() |
(1) | 0.03 | 9 | 6 | |
(2) | ![]() | 7 | 32 | |
(3) | 1 | 2 | 256 |
您最近一年使用:0次
20-21高二·全国·课后作业
解题方法
5 . 已知
为等比数列,填写下表:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
题次 | ![]() | q | n | ![]() |
(1) | 3 | ![]() | 5 | |
(2) | ![]() | 4 | ![]() | |
(3) | ![]() | 4 | ![]() | |
(4) | 3 | 5 | 48 | |
(5) | 3 | 2 | 24 |
您最近一年使用:0次
名校
解题方法
6 . 将
个数排成
行
列的一个数阵,如下图:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6b42a6527d536851721e2d6d1779f40.png)
该数阵第一列的
个数从上到下构成以
为公差的等差数列,每一行的
个数从左到右构成以
为公比的等比数列(其中
).已知
,
,记这
个数的和为
.给出下列结论:①
②
③
④![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ee24cb4787a625ef896018298b3a22.png)
其中结论正确的是______ .(填写所有正确答案的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ceef1abeeef220b4fe5f7d96feedd90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6b42a6527d536851721e2d6d1779f40.png)
该数阵第一列的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.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/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c20bc8da04fbb4bfea4e412274dde2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b73ec6f2aef5440b1b689fe74a8da96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ceef1abeeef220b4fe5f7d96feedd90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a3cc8c48bf54ec8252e5dce6867754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd9f9fa5a74a471d784caf42fa662a6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0367f5f840bf6ad1c1dc94049a326e26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ee24cb4787a625ef896018298b3a22.png)
其中结论正确的是
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名校
7 . 下列命题正确的是________ .(填写正确的序号)
①在等差数列
中,有
,则
;
②已知数列
是正项等比数列,且
,则
的值可能是
;
③已知函数
是定义在R上的奇函数,且对任意
,都有
成立,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9b6ed8cbd4162259985201ddfa4a049.png)
.
①在等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/788beef99e78bcb25b193a0e50362d9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c634e9a8afd9e6c931307dfaabb06810.png)
②已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3469ea4b3664ef316692458c96ac68d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
③已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87e04b4cd16224102ef696222caa56ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9b6ed8cbd4162259985201ddfa4a049.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afcc9c8a1885dad421eb332afc8c6039.png)
您最近一年使用:0次
2020-11-20更新
|
194次组卷
|
2卷引用:江西省赣州市十五县(市)十六校2021届高三上学期期中联考数学(文)试题
名校
8 . 如图,下面的表格内的数值填写规则如下:先将第1行的所有空格填上1;再把一个首项为1,公比为
的数列
依次填入第一列的空格内;其它空格按照“任意一格的数是它上面一格的数与它左边一格的数之和”的规则填写
(1)设第2行的数依次为
,试用
表示
的值;
(2)设第3列的数依次为
,求证:对于任意非零实数
,
;
(3)能否找到
的值,使得(2)中的数列
的前
项
成为等比数列?若能找到,
的值有多少个?若不能找到,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
第1列 | 第2列 | 第3列 | … | 第 | |
第1行 | 1 | 1 | 1 | … | 1 |
第2行 | |||||
第3行 | |||||
… | … | ||||
第 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e3d172f08313520e76b6cbc2ff9980c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05efa45c7e0cb072bc50414d5b3af20c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe3c7a8aa20a4d8f59e069331588a8bf.png)
(2)设第3列的数依次为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab48fb927796e4255ce8da7084366f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e8ca54783c66b05d71041fea750943.png)
(3)能否找到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab48fb927796e4255ce8da7084366f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca95e4940cdfab892b9f75620848852e.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
9 . 已知数列
为等比数列,其前
项和为
,且公比
;数列
为等差数列,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c3d80ac6c1a579eececfca16f0a55.png)
__________
.(填写“
”,“
”或“
”)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.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/d2b429d189e2b9fe22e55e82d0f831a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/761f70e0d9cc81e15654790a10b1767a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c3d80ac6c1a579eececfca16f0a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d98be54935b736c6c917feb9c5913e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/392cdb9d30684cce244bef94b8d861b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff7942da6c3fc4005256fb1458557c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6706fe00b4e231e62d9ecbec567d526b.png)
您最近一年使用:0次
2017-11-07更新
|
835次组卷
|
2卷引用:河南省郑州市一中2017-2018学年高二年级上学期期中模拟数学试题