名校
1 . 已知
为等差数列
的前n项和,
,则
( )
![](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/12a59b6d44509728b04821c38e4f0771.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9334dc3344670bf8962c98f7893a969e.png)
A.4 | B.6 | C.8 | D.10 |
您最近一年使用:0次
2022·全国·模拟预测
名校
解题方法
2 . 已知
为等比数列
的前n项和,若
,
,
成等差数列,且
.
(1)求数列
的通项公式;
(2)若
,且数列
的前n项和为
,证明:
.
![](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/e4b32aee86109b777671cd62868db3b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86e2e42b4aa93db9241103e7f61766c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3fc854e1dd70727f12571df8c4a54c9.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/716d59cee712c22885b6608848980b75.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/8195c685bcd7d2a14675625beec0d027.png)
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2022-12-05更新
|
4280次组卷
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13卷引用:云南省昆明市第三中学2023届高三上学期12月月考数学试题
云南省昆明市第三中学2023届高三上学期12月月考数学试题山西省山西大学附属中学2024届高三上学期9月月考(总第三次)数学试题吉林省通化市梅河口市第五中学2023-2024学年高三上学期9月月考数学试题四川省眉山市仁寿县仁寿县铧强中学2023-2024学年高三上学期10月月考数学试题四川省眉山市仁寿县铧强中学2023-2024学年高三上学期10月诊断性考试文科数学试题湖南省邵阳市邵东一中2024届高三上学期第四次月考数学试题福建省龙岩市第一中学2024届高三上学期第三次月考数学试题(已下线)2023年普通高等学校招生全国统一考试数学领航卷(二)(已下线)专题05 数列放缩(精讲精练)-1(已下线)新高考卷04四川省江油市太白中学2022-2023学年高三下学期高考模拟(三)数学试题吉林省白山市抚松县第一中学2023届高考模拟预测数学试题安徽省淮北市树人高级中学2023-2024学年高二上学期12月阶段测试数学试题
名校
解题方法
3 . 已知单调递增的等比数列
中,
,且
,
,
成等差数列,设数列
的前
项和为
,点
在抛物线
上.
(1)求数列
,
的通项公式;
(2)设
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b3175ab6772cd611f9c42771a9467d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455ccc1f06e91cb72efe6141afabf986.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25b67af73f586837594ab0db4b89baed.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)
您最近一年使用:0次
2021-01-19更新
|
800次组卷
|
3卷引用:河北省唐山市开滦第一中学2024届高三上学期12月月考数学试题
4 . 设数列
的前
项和为
,已知
、
、
成等差数列,且
.
(1)求
的通项公式;
(2)若
,
的前
项和为
,求使
成立的最大正整数
的值.
![](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/e72adb45c60c2f63b46e65ff787302bf.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/b1f6806b32ed102b69fe737492ec0c4d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acf999b026b5fc179a49f19bf068d3b3.png)
![](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/41a9eef61b347a03615162f572a068c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2020-11-23更新
|
1680次组卷
|
5卷引用:福建省厦门双十中学2021届高三12月月考数学试题
福建省厦门双十中学2021届高三12月月考数学试题重庆市第八中学校2021届高三上学期阶段性检测(3)数学试题安徽省皖豫名校联盟体2021届高三(上)第一次联考数学(文科)试题(已下线)调研测试三(B卷 滚动提升检测)-2021年高考数学(文)一轮复习单元滚动双测卷河北省唐山市第一中学2021届高三上学期期中数学试题
名校
5 . 设
是
与
的等差中项,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6da3c095f2305b90c1eb9e16565b95b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ffe4aba1f4253833d5231104d04183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef240df1da994718de42ec144a34c7cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f008cea432b68934066d32243ccf69bf.png)
A.![]() | B.3 | C.9 | D.![]() |
您最近一年使用:0次
2020-12-13更新
|
3523次组卷
|
6卷引用:山西省山西大学附属中学校2022届高三上学期9月(总第三次)模块诊断数学(文)试题
名校
解题方法
6 . 已知数列
满足:
,
数列
是等比数列,并满足
,且
,
,
成等差数列.
(1)求数列
,
的通项公式;
(2)若数列
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdcc44774d81a194c7b1f76deffae1ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385275d29d8c8a7841eaeaa3dfab2cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa13e39604bcacf54fe64fe54da8747d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a548938d87c80ac47910607d3857007f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15763959029e8bbc85bff7eead28e554.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25b67af73f586837594ab0db4b89baed.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/08eb71ecf8d733b6932f4680874dbbf3.png)
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2020-11-04更新
|
2037次组卷
|
5卷引用:安徽省安庆市宿松县程集中学2020-2021学年高三上学期9月月考数学(理)试题
名校
7 . 等比数列
满足
,数列
的前n项和为
,且
.
(1)求
和
的表达式;
(2)是否存在正整数m,使得
,
,
成等差数列?若存在,求出所有m的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25673902449184f5727cbc786aa82a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c65a658dc2dbc5aa141a49adc5068365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a00a7a6efb07e9a66809b988c3c65b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bd56c886d76991ec450d4aa1b7a6174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0f6000421c5370e4b89f23be199f388.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)是否存在正整数m,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5606524a0b5be8d429bf1da36aa02de8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7732fa58ee6b83ff15c81af8a758d8bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3c69b2580322e46d091ac44accf7d0b.png)
您最近一年使用:0次
名校
8 . 已知数列
中,
.若
为等差数列,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/d340caad1a98632cf41f029701e68ac4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dbd9ff686703cad03aa383e5fec21.png)
您最近一年使用:0次
2020-12-27更新
|
801次组卷
|
5卷引用:广东省六校联盟2021届高三上学期第二次联考数学试题
名校
解题方法
9 . 已知
是首项为1的等比数列,若
,
,
成等差数列,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e43966e36f658f7a347c346084588f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/604fbee0544dc18d9b15d5243dad9f2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39222f0687c9124bddb35544bcc7798.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
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2020-08-15更新
|
871次组卷
|
3卷引用:河北省衡水市枣强中学2020届高三下学期3月调研数学(理)试题
名校
10 . 设公差不为
的等差数列
的前
项和为
.若
,则在
、
、
、
这四个值中,恒等于
的个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8295a0d9267791b13632d223c0436050.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b53c211eecfe7c449b52ace8aef55d58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fb035fe568e25a250beeba0d75b5c59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a198c9856eff3a58a99c975e8630e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/151532f02f7519599c0436e47174850a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2020-05-29更新
|
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|
3卷引用:安徽省淮北市第一中学2020届高三下学期第八次月考数学(理)试题