1 . 将1,2,3,4,5,6,7,8,9这九个数填入如图所示
的正方形网格中,每个数填一次,每个小方格中填一个数,考虑每行从左到右,每列从上到下,两条对角线从上到下这8个数列,给出下列三个结论:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/2/a1197d5c-e308-484e-8bd3-99217fca01ed.png?resizew=65)
①这8个数列中最多有3个等比数列;
②若中间一行、中间一列、两条对角线均为等差数列,则中心数必为5;
③若第一行、第一列均为等比数列,则其余6个数列中至多有1个等差数列.
其中所有正确结论的序号是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/777d8fccf0cf8b55a68488fe48b78744.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/2/a1197d5c-e308-484e-8bd3-99217fca01ed.png?resizew=65)
①这8个数列中最多有3个等比数列;
②若中间一行、中间一列、两条对角线均为等差数列,则中心数必为5;
③若第一行、第一列均为等比数列,则其余6个数列中至多有1个等差数列.
其中所有正确结论的序号是
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解题方法
2 . 已知数列
是等比数列,若数列
的前4项和为
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7999465d0e871febde66296a0cbf058c.png)
____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caa585b9257ed0798213a9ae9b87d291.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9380bb008005f00edaf6ff90272277d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7999465d0e871febde66296a0cbf058c.png)
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名校
3 . 已知在等比数列
中,
、
分别是函数
的两个驻点,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dbd9ff686703cad03aa383e5fec21.png)
_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fd71bc7e6668f90f259ad0b06dd60c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d49c222678c9ea3603158e08cb8f326.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dbd9ff686703cad03aa383e5fec21.png)
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2023-04-14更新
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4卷引用:上海市闵行区2023届高三二模数学试题
上海市闵行区2023届高三二模数学试题(已下线)专题06 数列及其应用上海市青浦高级中学2023-2024学年高二下学期期中质量检测数学试卷(已下线)专题04数列--高二期末考点大串讲(沪教版2020选修)
4 . 写出一个通项公式![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
______ ,使你写出的数列
具有性质①②:
①
;②
为递减数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c5ef991d32c1b2d63ad876b6ad76882.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
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5 . 已知等比数列
的公比为q,且
,
,则q的取值范围为______ ;能使不等式
成立的最大正整数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1381f0937c6052ce088e0eaee7df4880.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33f7f603080feda2665bc02f43acb391.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e894a7f3b0bdb3d0947bc86ba08211c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
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2020-08-31更新
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8卷引用:重庆市第一中学2020届高三下学期适应性考试数学(理)试题
重庆市第一中学2020届高三下学期适应性考试数学(理)试题(已下线)专题2.2等比数列及其求和(B卷提升篇)-2020-2021学年高二数学必修五同步单元AB卷(人教A版,浙江专用)重庆市第一中学校2021届高三上学期第三次月考数学试题(已下线)2021届高三高考数学适应性测试八省联考考后仿真系列卷七(已下线)“8+4+4”小题强化训练(30)等比数列及其前n项和-2022届高考数学一轮复习(江苏等新高考地区专用)(已下线)一轮巩固卷02-【赢在高考·黄金20卷】备战2022年高考数学模拟卷(新高考专用)内蒙古阿拉善盟2023届高三第一次模拟考试数学(理)试题(已下线)专题7 等比数列的性质 微点1 等比数列项的性质
6 . 已知函数
,数列
是公比大于0的等比数列,且
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7999465d0e871febde66296a0cbf058c.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2d53e84446ab2d482dd8cdfeb27b402.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25131d323ad4304473cbd09ac0c1bb02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a65ccd88086eada17e6b169312569e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7999465d0e871febde66296a0cbf058c.png)
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2019-06-26更新
|
441次组卷
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3卷引用:上海市川沙中学2018-2019学年高一第二学期期末数学试题
7 . 数列
是以
为首项,
为公比的等比数列,数列
满足
,数列
满足
,若
为等比数列,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/466f052a797a7ad9711cee57f5208a4c.png)
__________ .
![](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/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8b3d61ccb35014e3cbf93f7af510d87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bcc423bd7f292372b6f47299572ee36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/466f052a797a7ad9711cee57f5208a4c.png)
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2019-06-12更新
|
304次组卷
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2卷引用:【全国百强校】贵州省南白中学(遵义县一中)2018-2019学年高一下学期期中考试数学试题
名校
8 . 设正项等比数列
的前
项和为
,若
,则
的最小值为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.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/bfc6da853bdd58024c67f45741e52e42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7d799d19d70dd143e5578d3975ff211.png)
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9 . 已知
是各项都为正数的等比数列,则前
项和为
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbfc875ca919921e8f63a6fca648561b.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.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/2570cec8ebbc4ebf384873ae7d7c0e00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbfc875ca919921e8f63a6fca648561b.png)
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2017-09-19更新
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4卷引用:广东省广州市海珠区2018届高三综合测试(一)数学理试题
12-13高三上·浙江台州·期末
10 . 若
是等比数列,
是互不相等的正整数,则有正确的结论:
.类比上述性质,相应地,若
是等差数列,
是互不相等的正整数,则有正确的结论:_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b511bcbe94aa484c0a067891fbf7968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7b33079c8fb634c6e98eb36b441a461.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b511bcbe94aa484c0a067891fbf7968.png)
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