2023高三·上海·专题练习
1 . 设等差数列
的前
项和为
,则
、
、
成等差数列.类比研究等比数列有下面三个命题:
①设等比数列
的前
项的和为
,则
、
、
成等差数列;
②设等比数列
的前
项的和为
,则
、
、
成等比数列;
③设等比数列
的前
项的积为
,则
、
、
成等比数列;
④设等比数列
的前
项的积为
,则
、
、
成等比数列.
其中真命题的个数是( )
![](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/0f30f56664446f32dbbc2c5f12a99374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1b0ed9533c1ea30a87249539a005e62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/648d3aceec8f1aff90191c20d7e51b2f.png)
①设等比数列
![](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/87bd7d18f67e90a7c37fad4252e43c9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91c08ee3ab8b691825d94fdb448868ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93b8b635d49a4a4beaf2c49d441352b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f214c8f5adbeb64d40ea387cec4d5f13.png)
②设等比数列
![](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/87bd7d18f67e90a7c37fad4252e43c9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91c08ee3ab8b691825d94fdb448868ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93b8b635d49a4a4beaf2c49d441352b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f214c8f5adbeb64d40ea387cec4d5f13.png)
③设等比数列
![](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/2114a0fe21dc0e5bf831c146ef02b113.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6dce0bc27993c08918cdffddcdee852.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0e39ed6588243d88450ec3ca4f0e9f1.png)
④设等比数列
![](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/2114a0fe21dc0e5bf831c146ef02b113.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7874208f32aeebb6ceaa2571408d9197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e2b24dbedb33be54b8095893f111cbb.png)
其中真命题的个数是( )
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2 . 在等差数列
中,若
,
,则
.类比此性质,在等比数列
中,
,
,可得
、
、
、
之间的一个不等关系为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9645bd4d2002993b90ec6d48f9c04f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ce64685821c3e55c07f151996ca8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/946fdb370ab639db644674b52c0464af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af0dd3fb6af23def773e1b0032a4f3c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eda6dc559d07bc22c9a0ed1e3a6d01d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a548938d87c80ac47910607d3857007f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64fcc69dc28bc11b22f5c9bec9e2aa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ada2c9f82459340da96274ee60ffbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0fcf02ab751cc3910a0bc0872ac2a7.png)
您最近一年使用:0次
3 . 下列推理正确的是( )
A.如果不买体育彩票,那么就不能中大奖,因为你买了体育彩票,所以你一定能中大奖 |
B.若命题“![]() ![]() ![]() |
C.在等差数列![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
D.如果![]() ![]() |
您最近一年使用:0次
21-22高二下·上海浦东新·阶段练习
名校
4 . 在共有2009项的等比数列
中,有等式
成立,类比上述性质,在共有2019项的等差数列
中,相应的有等式_________ 成立
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b2ab3bee5f49e83f6a4d448085235d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
您最近一年使用:0次
5 . 线性分形又称为自相似分形,其图形的结构在几何变换下具有不变性,通过不断迭代生成无限精细的结构.一个正六边形的线性分形图如下图所示,若图1中正六边形的边长为1,周长与面积分别记为
,
,图2中所有正六边形的周长之和与面积之和分别记为
,
,以此类推,图n中所有正六边形的周长之和与面积之和分别记为
,
,其中图n中每个正六边形的边长是图n-1中每个正六边形边长的
,则下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/2022/3/8/2931921057390592/2939137784922112/STEM/7bc8a3a64d0e4959ab1acabd12940f89.png?resizew=302)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://img.xkw.com/dksih/QBM/2022/3/8/2931921057390592/2939137784922112/STEM/7bc8a3a64d0e4959ab1acabd12940f89.png?resizew=302)
A.图4中共有294个正六边形 |
B.![]() |
C.![]() |
D.存在正数m,使得![]() |
您最近一年使用:0次
2022-03-18更新
|
426次组卷
|
2卷引用:河南省新乡市2021-2022学年高三上学期期末考试数学(文科)试题
21-22高二·江苏·课后作业
解题方法
6 . 对任意的等差数列
,计算
,
,
,
,…你发现了什么一般规律?能将发现的规律推广吗?在等比数列中有怎样类似的结论?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e6f19b84484b5480ea2100165abfd81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ab5a181478e9c2307d9a934d891621d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c273b7656ae822a6d802c09396e49bcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc5262813142d25b25f43dcb119e627.png)
您最近一年使用:0次
名校
7 . 已知数列
为等差数列,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09c58bbcaed92ebcf0c348220b736198.png)
.类比等差数列的上述结论,对等比数列
,若
,则当
时可以得到![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c22c5d27b307c2d505b3882e8b0b81b5.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a3c7acbc1a01fa0153273a8aa0812fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09c58bbcaed92ebcf0c348220b736198.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ded63fa6f83bf2343fe8638a35bc0e3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48af59823083f98a46906eefac6cc12c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5390fa61883d31dfcc9942930e3e8719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e443574f8ccb2467ff11a8d0a19d8b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c22c5d27b307c2d505b3882e8b0b81b5.png)
您最近一年使用:0次
8 . 公差为
(
)的等差数列
中,
是
的前
项和,则数列
,
,
也成等差数列,且公差为
,类比上述结论,相应地在公比为
(
)的等比数列
中,若
是数列
的前
项积,则有________________ 也成等比数列,且公比为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/812be9806122241c476ba1db516c4823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.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/2d84b38776b362f7d952c88ce410cf95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/498cb7cdfb13582a36fbadbc9b8cdb52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a83404b85d3600574b94e8167340b41e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2221d8b8d5035075b04712d56eb4d5e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45482d31d1d7448c9f3922b4d2a55331.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/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
名校
9 . 在等差数列
中,若
,则有等式
(
且
)成立,类比上述性质,在等比数列
中,若
,则有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83dda756cca393b4480163274559fbdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eebdeb0b558ca4029c61cb63d1e45d04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/315e26bbddc78d660096ed5073ddce3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a70b95c53fb6655721e2a8c61f5c2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de5e72acc9563b77a34d99fe085cfc10.png)
A.![]() ![]() ![]() |
B.![]() ![]() ![]() |
C.![]() ![]() ![]() |
D.![]() ![]() ![]() |
您最近一年使用:0次
2021-09-13更新
|
2230次组卷
|
5卷引用:江西省宜春昌黎实验学校2020-2021学年高二3月月考数学(文)试题
江西省宜春昌黎实验学校2020-2021学年高二3月月考数学(文)试题(已下线)4.3.1-4.3.2 等比数列的概念及通项公式(课堂培优)-2021-2022学年高二数学课后培优练(苏教版2019选择性必修第一册)河南省南阳市第一中学2021-2022学年高二下学期第一次月考文科数学试题(已下线)专题8 数列江西省吉安市(安福二中、泰和二中、井大附中、吉安县三中、遂川二中)五校2021-2022学年高二下学期联考(期中考试)数学(文)试题
名校
10 . 在等差数列
中,若
,则有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5965e192539aa0ac16bfb1e21c312d33.png)
成立.在等比数列
中,若
,类比上述性质,得到的等式为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e96739da4933995aef9a5c3897ee60d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5965e192539aa0ac16bfb1e21c312d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b6a7e1bfba58a35e35625706f7d7e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de5e72acc9563b77a34d99fe085cfc10.png)
您最近一年使用:0次