名校
解题方法
1 . 北京天坛圜丘坛的地面由石板铺成,最中间的是圆形的天心石,围绕天心石的是9圈扇环形的石板,从内到外各圈的石板数依次为
,设数列
为等差数列,它的前
项和为
,且
,
,则
( )
![](https://img.xkw.com/dksih/QBM/2022/1/13/2893775135039488/2896413231554560/STEM/ac649898-e62a-41c0-842a-042834838567.png?resizew=472)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4832bb09c71bcb19b44a5394f30f2b98.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/039e449a6d9e76e0497bf2672740f801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b9eba619fd20aa0f1b94f439e8c6fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae9ad4e59d7081cf19021423a984bc29.png)
![](https://img.xkw.com/dksih/QBM/2022/1/13/2893775135039488/2896413231554560/STEM/ac649898-e62a-41c0-842a-042834838567.png?resizew=472)
A.189 | B.252 | C.324 | D.405 |
您最近一年使用:0次
2022-01-17更新
|
1414次组卷
|
14卷引用:天津市北辰区南仓中学2023-2024学年高二上学期第二次月考数学试题
天津市北辰区南仓中学2023-2024学年高二上学期第二次月考数学试题吉林省白城市通榆县第一中学校2022-2023学年高二上学期期末数学试题甘肃青海大联考2021-2022学年高三上学期文科数学试题吉林省白山市2021-2022学年高三上学期期末考试数学(文)试题全国一卷老高考地区部分学校2021-2022学年高三上学期1月联考理科数学试题陕西省2022届高三上学期元月联考理科数学试题新疆昌吉州2022届高三上学期第二次高考质量检测数学(文)试题新疆昌吉州2022届高三上学期第二次高考质量检测数学(理)试题甘肃省白银市靖远县2021-2022学年高三上学期期末考试数学(理)试题甘肃省白银市靖远县2021-2022学年高三上学期期末考试数学(文)试题广西桂林市、梧州市2022届高三高考联合调研(一模)数学(理)试题广西桂林市、梧州市2022届高三高考联合调研(一模)数学(文)试题四川省凉山州宁南中学2021-2022学年高一下学期第二次月考数学(文)试题(已下线)考向19等差数列及其前n项和(重点)-2
名校
2 . 已知等差数列
满足
,
,则公差![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c98c59cd4749afdd21e73529fc84323.png)
______ .
![](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/36ba808c24aeae6a2f34b98ae5ec04ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c98c59cd4749afdd21e73529fc84323.png)
您最近一年使用:0次
2023-08-14更新
|
618次组卷
|
2卷引用:天津市朱唐庄中学2022-2023学年高二下学期3月阶段性检测数学试题
名校
解题方法
3 . 若等差数列的前
项和为
,数列
是等比数列,并且
,
,
,
,
.
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59693a58b316b5b3ef284b4c644a3eba.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/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
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4 . 等差数列
满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b08a8c9baca410ef1464caf7f522aa4a.png)
__________ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af1f1b7e9e20d799ee3c06b89a0611c.png)
__________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8db59f9c799d7d10067eb81bdb88c191.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b08a8c9baca410ef1464caf7f522aa4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af1f1b7e9e20d799ee3c06b89a0611c.png)
您最近一年使用:0次
5 . 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
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/9b08c58baacec3cd0c0a06e267fa9ec5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4437c6bdb72403891aad57b0fc685d17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b9a0d7150fb24be3e28ef7f0e18be93.png)
您最近一年使用:0次
6 . 设
为等差数列
的前
项和,且
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cd228d062d4085e949535cc73bae014.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/c8657a9f3eec0c1b0efa818f778129e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdba8a48eec7c0b90e22fa478d8f0ca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cd228d062d4085e949535cc73bae014.png)
您最近一年使用:0次
7 . 已知等差数列
与正项等比数列
满足
,且
,
,
既是等差数列,又是等比数列.
(1)求数列
和
的通项公式;
(2)①令
,求数列
的前
项和
;
②若对任意的
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85444874c705666de9488286d3d61dd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/161a7b35d1812e6745ae7f7c540cf87a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b7f27ebcef70a3ebbbe8d2e53ea0896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c969826f605d65fcf0f7ecf2ff49d4c.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)①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/08eb71ecf8d733b6932f4680874dbbf3.png)
②若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0bef1ed5bfa0e29a7d03f773da37b5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
名校
解题方法
8 . 已知等差数列
的前n项和为
,公差
,且
,
,
,
成等比数列.
(1)求数列
的通项公式;
(2)设
是首项为1,公比为3的等比数列,
(ⅰ)求数列
的前n项和
;
(ⅱ)若不等式
对一切
恒成立,求实数
的最大值.
![](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/812be9806122241c476ba1db516c4823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9651204c54475c2e8cda8d0a6eeba177.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eca7e7b23fd74e3cf89ac541cb7a5d88.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9a6c852d593cb9f6bdfd9eeddb50fa3.png)
(ⅰ)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(ⅱ)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce70396e9a9c2268109b4acb3a23045.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2024-01-18更新
|
543次组卷
|
3卷引用:天津市滨海新区2023-2024学年高二上学期期末质量检测数学试题
名校
解题方法
9 . 已知等差数列
的前
项和为
,且
.
(1)求数列
的通项公式;
(2)记
,求数列
的前
项和
.
![](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/8439fe8fcaea5550194f3245255121a2.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9ebf05ca12f9da810b2b10e066ececf.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)
您最近一年使用:0次
名校
10 . 已知数列的前
项和为
,
,且
,
,则当
取得最大值时,
( )
A.7 | B.8 | C.9 | D.10 |
您最近一年使用:0次