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1 . 等比数列
的各项均为正数,其前n项和为
,已知
,
,则
( )
![](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/22ab4706be6b3854b9c30ab609e5da68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c289a2664633d3b8d43eeffc90dcae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0382b4a2ab0657d2d6830bb6be2b17b6.png)
A.![]() | B.32 | C.64 | D.![]() |
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8卷引用:吉林省长春外国语学校2021-2022学年高二下学期期初考试数学试题
吉林省长春外国语学校2021-2022学年高二下学期期初考试数学试题(已下线)2022年全国高考乙卷数学(文)试题变式题1-4题福建省福安市第一中学2022-2023学年高二上学期第一次月考数学试题(已下线)2022年全国高考乙卷数学(文)试题变式题9-12题(已下线)第四章:数列重点题型复习(1)(已下线)4.3.2 等比数列的前n项和公式(1)(已下线)模块二 专题6《数列》单元检测篇 A基础卷 (人教A)(已下线)1.3.2 等比数列的前n项和5种常见考法归类(1)
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2 . 十七世纪德国著名的天文学家开普勒曾经这样说过“几何学里面有两件宝,一个是勾股定理,一个是黄金分割,如果把勾股定理比作金矿的话,那么可以把黄金分割比作砖石,”黄金三角形有两种,其中底与腰之比为黄金分割比的黄金三角形被认为最美的三角形,它是一个顶角为
的等腰三角形(另一种是顶角为
的等腰三角形),如图所示的五角星由五个黄金三角形与一个正五边形组成,在其中一个黄金
中,
,根据这些信息可得到
( )
![](https://img.xkw.com/dksih/QBM/2022/3/1/2926965973352448/2933165468925952/STEM/42415f22-54b1-4e46-977a-099e02de884f.png?resizew=188)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8ac0ea8ecb56b0ca8943509dd2b5657.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26c1e27ff08d4fdfff5a5395a1c6e237.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38abf0af6b05e7fd67b5c5de765675c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/273a1cc69a748331f3e28c0d360a2b9c.png)
![](https://img.xkw.com/dksih/QBM/2022/3/1/2926965973352448/2933165468925952/STEM/42415f22-54b1-4e46-977a-099e02de884f.png?resizew=188)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
3 . 已知
,
满足不等式组
,则目标函数
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0784e15260760a3ef0f832aeef7f9bdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee51b0cac927e6445e4b94438c2ff3da.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 已知数列
是首项为1的等差数列,数列
满足
,且
,
.
(1)证明数列
是等比数列并求
的通项公式;
(2)令
,求数列
的前
项和
![](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/1857d02529cce9ad6d1f80dc5c0f3bdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/368dc84a523ce87b9962505c06a9bfd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
(1)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36676cd8165b9136b1127e73565dac0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29518f13a1ebc3fff8181c2d7cfba22f.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9221c0c92a526f65533cdc5400767af.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)
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5 . 两个等差数列![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7c65b27d8a960659cb02151cb31c112.png)
则
=( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7c65b27d8a960659cb02151cb31c112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e80c43eb141cd568a48badc0a7a5363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/265397c51288caa8df9b42f1f698b5a5.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
6 . 已知数列
的前n项和为
,且
,
.
(1)证明:数列
是等比数列,并求数列
的通项公式;
(2)若数列
的前n项和为
,
,且
,
,是否存在正整数k,使得
且
?若存在,求出k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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68cc6414ac77edb084a13b5ea9f2867f.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若数列
![](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/af933982377238c8931570df5918c723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99622e8a419c74a9d417451ee16b9745.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f9de120173566422c32546c783789fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40035c0235c6ab19e05dde77e7ca64d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5928fc74d6331edb7f2abc9b706bccc.png)
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7 . 已知数列
是等比数列,
,
,
成等差数列,则数列
的公比q=___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0d4dad2cc2f2ca8a60a86f11ce7cb8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/911278aa8595846abac1972e1de59995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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3卷引用:吉林省长春市第二实验中学2021-2022学年高二下学期开学考试数学试题
吉林省长春市第二实验中学2021-2022学年高二下学期开学考试数学试题吉林省通化市梅河口市第五中学2021-2022学年高二上学期期末数学试题(已下线)第4章 数列(基础30题专练)-2021-2022学年高二数学考试满分全攻略(人教A版2019选修第二册+第三册)
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解题方法
8 . 设首项大于0的数列
的前n项和为
,若
,
,则下列说法正确的是( )
![](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/23ff0a19f71121c415a95a60f86ab9c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0ca5bc440491fd3a5df71dd55086632.png)
A.![]() | B.![]() |
C.![]() ![]() | D.使![]() |
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解题方法
9 . 已知数列
,
满足:
,
,则数列
的前9项和为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f90d16df7d38c851b2619785aff282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c46926541ba7475097cdb971a04d371b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
A.1022 | B.99 | C.90 | D.45 |
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10 . 在等差数列
中,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/072b9dd6a9ca84a8d99182c7da47a3bd.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e092b570aae02d47e913747e2433584b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/072b9dd6a9ca84a8d99182c7da47a3bd.png)
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