解题方法
1 . 数列
的前n项和![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c959114e77e1793389ddcf4c7c8f232f.png)
,数列
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2036cb05aa65cff20c657ed53b38c5c2.png)
,则数列
中值最大的项和值最小的项和为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c959114e77e1793389ddcf4c7c8f232f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae630ae7b2e9d266a23fe34616a13a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2036cb05aa65cff20c657ed53b38c5c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca62adc6c3fe53b3f49fb80d5f76aced.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
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解题方法
2 . 已知数列
满足
,
数列
前
项和为
,则下列叙述正确的有( )
![](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/31a3c7fe45d488eb402cd86aea0ee9b9.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)
A.![]() | B.![]() |
C.![]() | D.![]() |
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3 . 已知数列
满足:
,
.
(1)证明:数列
是等差数列;
(2)设
,求数列
的前n项和
.
![](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/83f2918a23de2898a1910d30215e2395.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dff5da661fc56135bebd848b282868e.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/327c5aed6d1e069c9449edd65cc28f8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2022-11-19更新
|
2384次组卷
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4卷引用:吉林省长春市2023届高三上学期质量监测(一)数学试题
吉林省长春市2023届高三上学期质量监测(一)数学试题(已下线)专题04 数列的通项、求和及综合应用(精讲精练)-1(已下线)数学(新高考Ⅰ卷B卷)天津市河东区2022-2023学年高二上学期期末数学试题
名校
解题方法
4 . 已知数列
满足
,
,记数列
的前
项和为
,则
=( )
![](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/3b64b33a83519d07172a00aacc7119b7.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/adf8b578e17af6532bf6e7866592b800.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
解题方法
5 . 设正项数列
的前n项和为
,且
.
(1)求
的通项公式;
(2)设
,求数列
的前n项和
.
![](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/9e3c39732b34ee1f58803822e37b6b8a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfea72a1bdd749b13be2f8947b78c0ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2022-06-21更新
|
816次组卷
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3卷引用:辽宁省葫芦岛市协作校2021-2022学年高二下学期第一次联考数学试题
名校
解题方法
6 . 已知数列{
}为等差数列,
,
,数列{
}的前n项和为
,且满足
.
(1)求{
}和{
}的通项公式;
(2)若
,数列{
}的前n项和为
,且
对
恒成立,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2693734765399876e9e93cdb110231c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f86cc1dbf9768a7f7a487517ea7224d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f61d6a6b7579718b63724b734b9c1278.png)
(1)求{
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9221c0c92a526f65533cdc5400767af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e89c08f1032d49b57607e3af5c2f294f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
您最近一年使用:0次
2022-06-03更新
|
3190次组卷
|
9卷引用:湖南省长沙市长沙县第一中学2022届高三下学期押题卷4数学试题
湖南省长沙市长沙县第一中学2022届高三下学期押题卷4数学试题(已下线)第06讲 第六章 数列综合测试(测)-2023年高考数学一轮复习讲练测(新教材新高考)(已下线)专题18 等差数列及其求和(讲义)-2023年高考数学一轮复习精讲精练宝典(新高考专用)(已下线)专题27 数列求和-1(已下线)专题12 数列综合辽宁省沈阳市辽中区第二高级中学2021-2022学年高二下学期期末考试数学试题(已下线)第7讲 数列求和9种常见题型总结 (1)(已下线)模块四 专题2 期末重组综合练(辽宁)(高二人教B)广东省深圳市光明区光明中学2023-2024学年高二下学期期中考试数学试题
7 . 数列
满足:
或
.对任意
,都存在
,使得
,其中
且两两不相等.
(1)若
,写出下列三个数列中所有符合题目条件的数列的序号;
①
;②
;③![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6682443f327ff60ddf3e91cbe7821d99.png)
(2)记
.若
,证明:
;
(3)若
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32034ab9eaa06e450e27d87e999ea9e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bad657749a0e222333076c72bf949970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fdb0c5b7a3e183c714fad838d246d29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c639c7e5f1e7e7ee5d5ee2f30b155bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b056a90a2751f04ba5fff3dc5c1d0674.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86c4d0383577207858e39b4b19b0853e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/454cc6ac47d35ebc2b34af6a8047a44e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94f16d5ed858699bfea5039a7bf8ae6.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5305ea58d22efe7136d404b1d44634.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e44f2f5b6cab3a33e24de2502ac0c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6682443f327ff60ddf3e91cbe7821d99.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6559598727fb120a5cdbf4f15510615d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a3cc8c48bf54ec8252e5dce6867754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/743b4f6fde34464397b010cb45eabb7d.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662276a5012893d881e7d1d882b5ea4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2022-05-29更新
|
536次组卷
|
9卷引用:北京市西城区2018届高三期末考试理科数学试题
8 . 已知数列
是公比
的等比数列,前三项和为13,且
,
,
恰好分别是等差数列
的第一项,第三项,第五项.
(1)求
和
的通项公式;
(2)已知
,数列
满足
,求数列
的前2n项和
;
(3)设
,求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eda6dc559d07bc22c9a0ed1e3a6d01d2.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)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cad52924df9291d5d191d18e09374ee1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e90c4e8734cf9695378e52862a603900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b9a0d7150fb24be3e28ef7f0e18be93.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c910871ff511e1ea952ad66eff1016db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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2022-05-27更新
|
3496次组卷
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12卷引用:天津市南开区2022届高三下学期三模数学试题
天津市南开区2022届高三下学期三模数学试题(已下线)专题27 数列求和-2天津市第七中学2022-2023学年高三上学期12月月考数学试题天津市南开区翔宇学校2022-2023学年高三上学期期末数学试题天津市南开大学附属中学2023届高三下学期2月统练(一)数学试题(已下线)天津市南开中学2023届高三下学期第五次月考数学试题(已下线)第7讲 数列求和9种常见题型总结 (2)(已下线)专题6-2 数列大题综合18种题型(讲+练)-1(已下线)模块六 专题6 全真拔高模拟2(已下线)数列 求和专题04数列求和(裂项求和)天津市滨海新区塘沽第一中学2023-2024学年高二上学期期末数学练习9
9 . 已知数列
满足
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f5eb9b8f893dd71876349ad40724550.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59b33897f206bf6e08dc4460aad97288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2da0ff9dc73d62f8162fc3de186150.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f5eb9b8f893dd71876349ad40724550.png)
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2022-04-29更新
|
639次组卷
|
3卷引用:重庆市西南大学附属中学校2021-2022学年高二下学期期中数学试题
名校
10 . 已知数列{an}满足
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d754bc529cfab94af50384ef686b191d.png)
A.{an}是递增数列 | B.![]() |
C.![]() | D.![]() |
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2022-03-11更新
|
1308次组卷
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6卷引用:福建省厦门市2022届高三毕业班3月第二次质量检测数学试题