1 . 已知数列
为等差数列,
,
,数列
满足
,
(1)求证:数列
为等比数列;
(2)求数列
的前n项的和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab4cfe3057df9a8047c35a74631e5e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/605651764b7789d370f96f1e4f0f4623.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5344eadd4711db34e3f935aedd5fb270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2023-02-23更新
|
453次组卷
|
4卷引用:广东省广州市荔湾区2022-2023学年高二下学期教学质量调研数学试题
2 . 已知数列
的前n项和为
,
,给出以下三个条件:①
;②
是等差数列;③
.
(1)从三个条件中选取两个,证明另外一个成立;
(2)利(1)中的条件,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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6e35ba37b0cc1d390e05391554e9660.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de90af6e18cba1b927bcdf234365a615.png)
(1)从三个条件中选取两个,证明另外一个成立;
(2)利(1)中的条件,求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4713b163b429661468190a86f160b39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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2023-07-05更新
|
300次组卷
|
7卷引用:广西三新联盟2022-2023学年高二下学期5月期中联考数学试题
广西三新联盟2022-2023学年高二下学期5月期中联考数学试题(已下线)专题1 全真基础模拟1(人教A版)(已下线)模块三 专题9 劣构题专练--基础夯实练)(人教A版)(已下线)专题1 全真基础模拟1(北师大2019版)(已下线)模块三 专题8 劣构题专练--拔高能力练(人教B版)(已下线)模块三 专题9 劣构题专练--基础夯实练)(北师大2019版 高二)(已下线)模块三 专题3 高考新题型专练(专题1:劣构题专练)(北师大)(高二)
名校
解题方法
3 . 已知数列
的前
项和为
, 且
, __________.请在
成等比数列;
, 这三个条件中任选一个补充在上面题干中, 并解答下面问题.
(1)求数列
的通项公式;
(2)设数列
的前
项和
, 求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751c3b0c7d916ddc24d7bd036ea0eecd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4011c597ba394120a1a74b6f4a401159.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25108967f8f95c445c109348592d4fee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff3432f48e3f2e684d45e89403110ea9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9694346716bad8031f17fff37273ddc.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751c3b0c7d916ddc24d7bd036ea0eecd.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55f3cadcc65d380f74102037b46a4f8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59887a5ab83d604d78b8a204b7f88bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24974f2d84f24c6dc2d836e0d9fa5359.png)
您最近一年使用:0次
2022-12-26更新
|
849次组卷
|
7卷引用:数列求和
(已下线)数列求和广东省揭阳市普宁国贤学校2022-2023学年高二上学期期末数学试题山西省晋城市泽州县晋城一中教育集团南岭爱物学校2022-2023学年高二上学期1月期末调研考试数学试题四川省南充市2021-2022学年高三高考适应性考试(一诊)数学(理)试题(已下线)热点07 数列与不等式-2022年高考数学【热点·重点·难点】专练(新高考专用)湖南省岳阳市2022届高三下学期教学质量监测(三)数学试题四川省遂宁市第二中学校2023届高三上学期一诊模拟考试理科数学试卷(二)
名校
解题方法
4 . 已知数列
为公差不为零的等差数列,其前n项和为
,
,
.
(1)求
的通项公式
;
(2)求证:
.
![](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/34e3012b669194c74b11a95c18bbf667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a7f8f1b5bff849c18f368df4f6764ce.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e60fbec842e9f7b352d0ba3ad641946f.png)
您最近一年使用:0次
2023-02-16更新
|
1878次组卷
|
5卷引用:江西省南昌市第十九中学2022-2023学年高二下学期期末考试数学试卷
江西省南昌市第十九中学2022-2023学年高二下学期期末考试数学试卷安徽省合肥市2023届高三下学期第一次教学质量检测数学试题(已下线)模块九 数列-1(已下线)专题10数列(解答题)新疆乌鲁木齐市第十二中学2024届高三下学期5月月考数学试题
解题方法
5 . 已知等差数列
的公差
不为
,
,且
,
,
成等比数列.
(1)求数列
的前
项和
;
(2)记
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a0d29f34218cd60cc6e9ce4dcd13925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eca7e7b23fd74e3cf89ac541cb7a5d88.png)
(1)求数列
![](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)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c887a833169ee4f128e193570c07ca3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44071ad4a95e849ed510c8e91bd575b0.png)
您最近一年使用:0次
2023-07-08更新
|
251次组卷
|
3卷引用:湖南省邵阳市2022-2023学年高二下学期7月期末联考数学试题
6 . 已知数列
的首项
.
(1)从下面①②③中选取两个作为条件,证明另外一个成立.
①
;②
是等差数列;③
;
(2)利用(1)中的条件,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)
(1)从下面①②③中选取两个作为条件,证明另外一个成立.
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6e35ba37b0cc1d390e05391554e9660.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de90af6e18cba1b927bcdf234365a615.png)
(2)利用(1)中的条件,设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/288d4efab50964b9b9d5fba3f1d22fc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.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
解题方法
7 . 在单调递增的等差数列
中,
,
,
成等比数列,
.
(1)求数列
的通项公式;
(2)设数列
的前
项和为
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.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/46be9c9b05fd84ac9256d49a5a553af5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a0eecb5b800fce9ae10aed86ffee62.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设数列
![](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/b00f934ec9aa1208cb375e7559070880.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de284e39cfb3621ee94089d5d0bfe32.png)
您最近一年使用:0次
8 . 已知
为等差数列,
,记
,
分别为数列
,
的前n项和,
,
.
(1)求
的通项公式;
(2)证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e9840fce9bc9f6bfd4ca69295c133d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](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/19181548bcfbfe7a38a2c84096199563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf068678969571e78425d6f279cd1995.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45deada38f235bf0efb327bc4477034a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90718ef497edb369828f4b8e323b10d7.png)
您最近一年使用:0次
2023-06-07更新
|
44312次组卷
|
46卷引用:专题05 等比数列与数列综合求和-2023-2024学年高二数学期末复习重难培优与单元检测(人教A版2019)
(已下线)专题05 等比数列与数列综合求和-2023-2024学年高二数学期末复习重难培优与单元检测(人教A版2019)湖南省衡阳市第八中学2023-2024学年高二创新班上学期第一阶段测试数学试题(已下线)重难点03:数列近3年高考真题赏析-2023-2024学年高二数学同步精品课堂(北师大版2019选择性必修第二册)(已下线)重难点02:求数列前n项和常用10种解题策略-2023-2024学年高二数学同步精品课堂(北师大版2019选择性必修第二册)2023年新课标全国Ⅱ卷数学真题(已下线)2023年高考数学真题完全解读(新高考Ⅱ卷)专题05数列(成品)专题05数列(添加试题分类成品)专题05数列(成品)(已下线)专题11 数列前n项和的求法 微点8 分组法求和(已下线)2023年新课标全国Ⅱ卷数学真题变式题15-18(已下线)专题07 数列-1(已下线)模块一 情境3 以数列为背景(已下线)重难专攻(五) 数列中的综合问题(讲)山西省晋城市第一中学校2024届高三上学期8月月考数学试题江西省宜春市宜丰县宜丰中学2023-2024学年高三上学期9月月考数学试题天津市耀华中学2024届高三上学期第一次月考数学试题福建省厦门第二中学2024届高三上学期第二次阶段性考试(10月)数学试题北京市景山学校2024届高三上学期10月月考数学试题(已下线)第05讲 数列求和(练习)(已下线)第02讲 等差数列及其前n项和(十大题型)(讲义)-2(已下线)第04讲 数列的通项公式(练习)-2(已下线)天津市耀华中学2024届高三上学期第一次月考数学试题变式题16-20(已下线)考点3 等差列的前n项和及其性质 2024届高考数学考点总动员(已下线)考点12 数列中的不等关系 2024届高考数学考点总动员(已下线)第2讲:复杂数列通项和求和【练】(已下线)第3讲:数列中的不等问题【练】(已下线)专题04 数列及求和(讲义)(已下线)专题10 数列不等式的放缩问题 (7大核心考点)(讲义)(已下线)专题05 数列 第三讲 数列与不等关系(解密讲义)(已下线)专题05 数列 第二讲 数列的求和(解密讲义)(已下线)专题05 数列 第二讲 数列的求和(分层练)(已下线)专题29 等差数列通项与前n项和(已下线)专题6.1 等差数列及其前n项和【九大题型】(已下线)重难点10 数列的通项、求和及综合应用【九大题型】(已下线)专题06:数列大题真题精练(已下线)专题09 数列的通项公式、数列求和及综合应用(练习)-2天津市九校2024届高三下学期联合模拟考试(一)数学试卷(已下线)FHgkyldyjsx15(已下线)专题21 数列解答题(理科)-3(已下线)专题21 数列解答题(文科)-2(已下线)专题2 考前押题大猜想6-10江苏省无锡市锡东高级中学2024届高三下学期5月月考数学试题专题06数列(已下线)五年新高考专题06数列(已下线)三年新高考专题06数列
9 . 已知正项等差数列
前
项和为
,______,
.请从条件①
,
;条件②
,且
,
,
成等比数列,两个条件中任选一个填在上面的横线上,并完成下面的两个问题.
(1)求数列
的通项公式;
(2)记数列
的前
项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d1a511265fdde77ed111876f337458.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/684397f1d22e673aad2d2edb3476ac7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db2c97f55d9ffac66e05017b38c05b9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36989853e0d247e504b292e17d8a8cfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/614206299653e4111ac285f5375e34c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d1a511265fdde77ed111876f337458.png)
(2)记数列
![](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/554bc513d6fc6f03128925d4208d8beb.png)
您最近一年使用:0次
解题方法
10 . 设等差数列
的前
项和为
,且
,
.数列
满足
,
,
(1)求数列
的通项公式;
(2)求证:数列
是等比数列;
(3)求数列
(
为正实数)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/ae2e6956e0073cef684fef6a16bead0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cde13a1d82174255f34cc22f8127787b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a02563c38f1e5c8fd724af9d6f22563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deda945164283569437cda6976fe35ea.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9a6c852d593cb9f6bdfd9eeddb50fa3.png)
(3)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd7f41822ee607b5dde87bdb13daca84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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