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1 . 若数列
是等差数列,且
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ce2d03b64e6ceead9db069da95ec3b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3307c60261fc079f584347a8d404551.png)
A.48 | B.50 | C.52 | D.54 |
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2024-02-20更新
|
570次组卷
|
3卷引用:广东省佛山市南海区南执高级中学2023-2024学年高一下学期第一阶段测数学试题
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2 . 在各项均为正数的等比数列
中,
,且
,
的等差中项为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ebce85ea9bc18815ef8887057030a63.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e475b58009937a2660442beecb0faa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ebce85ea9bc18815ef8887057030a63.png)
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解题方法
3 . 若数列
满足
(
),且
,
,则当
的前n项和取到最大值,n的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b3dcec91897ae20800fb6912b207ed6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/366dfedff1a1a96ec27650375b680059.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/768fef3a7ee776a663424916c1fa968c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
A.5 | B.6 | C.7 | D.8 |
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4 . 若正四面体
的棱长为3,平面ABC内有一动点P到平面
、平面
、平面
的距离依次成等差数列,则点P在面
内的轨迹的长度为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/334a5773c8d24f29ec3231075170e4f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9c9cfa597b444b5c9dbae7a825a695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21665d21bbfb04410c78345de1fd15ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/482465f00a75da723e425dbbef2f0bfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
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解题方法
5 . 已知在
中,角
的对边分别为
,则下列四个结论中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
A.若![]() ![]() |
B.若![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() |
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解题方法
6 . 已知
为等差数列
的前
项和,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07faf3d825a256ad497f5a74ec6745e.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/9f4d50bc5dfb09fcf888e70aa0ecc1ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07faf3d825a256ad497f5a74ec6745e.png)
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解题方法
7 . 数列
满足
,
是常数.
(1)当
时,求
及
的值;
(2)数列
是否可能为等差数列?若可能,求出它的通项公式;若不可能,说明理由;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b72c1ffacd813446fa9670b78e710680.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7def23f30138e0b7c4c1e498d6903a6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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8 . 公元263年,刘徽首创了用圆的内接正多边形的面积来逼近圆面积的方法,算得
值为3.14,我国称这种方法为割圆术,直到1200年后,西方人才找到了类似的方法,后人为纪念刘徽的贡献,将3.14称为徽率.我们作单位圆的外切和内接正
边形
,记外切正
边形周长的一半为
,内接正
边形周长的一半为
.通过计算容易得到:
(其中
是正
边形的一条边所对圆心角的一半)
(1)求
的通项公式;
(2)求证:对于任意正整数
依次成等差数列;
(3)试问对任意正整数
是否能构成等比数列?说明你的理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbbc0cf9164007ddd298dd2236703f2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bbccb799ae7eb992b25b2426173ed36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbbc0cf9164007ddd298dd2236703f2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbbc0cf9164007ddd298dd2236703f2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96936fc2a366e6a8d1dfae54322d5d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92ffa8be5a02790c6161c56b8e90db64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbbc0cf9164007ddd298dd2236703f2f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求证:对于任意正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac64c640ccd57708681eada27a8fa6d.png)
(3)试问对任意正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8e42bf4d8449d427c1f5f252db0f298.png)
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2023-07-21更新
|
386次组卷
|
3卷引用:上海师范大学附属中学2022-2023学年高一下学期期末数学试题
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9 . 下列说法正确的是( )
A.若![]() ![]() ![]() ![]() |
B.在![]() ![]() ![]() ![]() ![]() |
C.三个不全相等的实数![]() ![]() ![]() ![]() ![]() ![]() |
D.![]() ![]() ![]() |
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10 . 已知等差数列
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07ed39d9d163bcdde78d488fed83ffcf.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f1e55cb07aa8350755e0e4f54ca0fe3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68670cdec38839f18fa602bfe3dc6c0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07ed39d9d163bcdde78d488fed83ffcf.png)
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