1 . 已知数列
是公差为1的等差数列,且
,数列
是等比数列,且
.
(1)求
和
的通项公式;
(2)令
,求证:
;
(3)记
其中
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecd2edf101d891d5471a0848ebbcf65f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cc3dbc001729162ac54c0134f000a3c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe18b02a93934205223805180ddad10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/965a6530b8a92f753cd6efdfd8be392f.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e71bd169e5b0a0b445572b7a65c28106.png)
![](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/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b9a0d7150fb24be3e28ef7f0e18be93.png)
您最近一年使用:0次
2 . 已知数列
满足:
,正项数列
满足:
,且
,
,
.
(1)求
,
的通项公式;
(2)已知
,求:
;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9613f8aa0a503b83e25141127a19efe0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7bdaf9fa374c130456f462ee49c4ee1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ffaa768f1232ff14bcd2cdd438ce53a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1273751a0b5a984cf01c2d0e00e474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb27d03d22ec55dbf33d6d9d3c44854f.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/b97aef7af01785f58caee047c55187e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ca23ce02583bd8fe3b9d06d99e0e3c.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5fca0c9355067a7b3e8d60bf0573e40.png)
您最近一年使用:0次
2023-04-29更新
|
2735次组卷
|
8卷引用:天津市滨海新区塘沽第一中学2024届高三毕业班八校联考数学模拟试题
天津市滨海新区塘沽第一中学2024届高三毕业班八校联考数学模拟试题天津市十二区重点学校2023届高三下学期毕业班联考(二)数学试题天津市宁河区芦台第一中学2022-2023学年高二下学期5月学情调研数学试题(已下线)专题15 数列不等式的证明 微点6 数列不等式的证明综合训练(已下线)2023年天津高考数学真题变式题16-20福建省福州格致中学2024届高三上学期10月质检数学试题(已下线)数列与不等式专题04数列求和(裂项求和)
名校
解题方法
3 . 已知
为等差数列,前n项和为
,
是首项为2的等比数列,公比大于0,且
,
,
.
(1)求
和
的通项公式;
(2)求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/760f42da9081430c4c6b0e48c8bc6274.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3408df52e3c9d4b12392a1463bc6ad96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a597f2838a2e6975de78103256c5bc88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e66d67b5c93a1f8de640c6935505145.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2875f72cd781842d4b0cb0ac2b526aa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47a9d3586dcc7fd8bd5e90906b140813.png)
您最近一年使用:0次
2023-03-31更新
|
670次组卷
|
7卷引用:天津市西青区2019-2020学年高三第一学期期末考试数学试题
名校
解题方法
4 . 已知等差数列
的前
项和为
,若
,则
( )
![](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/daf736cfe877b89a0b5d98049426f2da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30eb42578f654fb61e826026d2199751.png)
A.33 | B.66 | C.22 | D.44 |
您最近一年使用:0次
2023-03-16更新
|
1746次组卷
|
12卷引用:天津市宁河区芦台第一中学2023-2024学年第一学期高三年级第一次诊断
天津市宁河区芦台第一中学2023-2024学年第一学期高三年级第一次诊断四川省巴中市2023届高三“一诊”考试数学(文)试题四川省巴中市2023届高三“一诊”考试数学(理)试题(已下线)专题10数列(选择填空题)(已下线)四川省巴中市2023届高三“一诊”考试数学(理)试题变式题1-5四川省乐山市金口河区延风中学2024年高三上学期9月月考数学(理科)试题黑龙江省牡丹江第二高级中学2023-2024学年高二上学期期末模拟数学试题辽宁省沈阳市郊联体2022-2023学年高二下学期4月月考数学试题河南省郑州市第三十一高级中学2022-2023学年高二下学期期中数学试题河南省南阳市第一中学校2022-2023学年高二下学期3月月考数学试题吉林省白城市通榆县毓才高级中学有限责任公司2022-2023学年高二下学期期中数学试题(已下线)模块四 专题2 期中重组篇(吉林卷)(人教B版高二下学期期中)
名校
解题方法
5 . 已知数列为各项均为正数的等比数列,
,
,则
的值为( )
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-03-10更新
|
1793次组卷
|
8卷引用:天津市河东区2024届高三上学期期末质量调查数学试题
天津市河东区2024届高三上学期期末质量调查数学试题河北省石家庄市2023届高三质量检测(一)数学试题四川省成都市简阳市阳安中学2023届高三下学期三诊模拟考试数学(文科)试题四川省成都市简阳市阳安中学2023届高三三诊模拟考试数学(理科)试题(已下线)河北省石家庄市2023届高三质量检测(一)数学试题变式题1-5江西省抚州市2022-2023学年高二下学期学生学业发展水平测试(期末)数学试题(已下线)4.3.2等比数列的前n项和公式(第1课时)(分层作业)(3种题型)-【上好课】高二数学同步备课系列(人教A版2019选择性必修第二册)广东省广州市铁一中学2023-2024学年高二下学期3月月考数学试题
6 . 已知
为等差数列,
是公比为
的等比数列,且
.
(1)证明:
;
(2)已知
.
(ⅰ)证明:
;
(ⅱ)求
.
![](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/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9577321bd85f232a0fecb06639171e90.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89fe0f4e8a80a2840c0f6929a8a6351b.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
(ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d84a12bd11dea6358891c97768ebb129.png)
(ⅱ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852b62a53dad21312caee3e7d5b3efc1.png)
您最近一年使用:0次
7 . 设双曲线
的焦距为
,若
成等差数列,则双曲线的渐近线方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8dcc91c2ffb5571eaf944c34f5e8ffe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d6e7e03305ce819a63b754cab365c6c.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2023-02-22更新
|
926次组卷
|
3卷引用:天津市河北区2022-2023学年高三上学期期末数学试题
8 . 已知等比数列
的前
项和为
,
是等差数列,
,
,
,
.
(1)求
和
的通项公式;
(2)设
的前
项和为
,
,
.求证:
.
![](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/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdd3a25ac2cde3d2c884028f750cfff8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/684b935a7274130d081bfa7b2b938023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c45994e58cc2032df1cc501e44ed17f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0b3874af2d1f4dcf456e5d24c4359a9.png)
(1)求
![](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/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/7db76422e0e75880dab2c22b549e1323.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deda945164283569437cda6976fe35ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1275fba3773580edb2a12e627b44f0b5.png)
您最近一年使用:0次
9 . 已知数列
是公差为2的等差数列,其前8项的和为64.数列
是公比大于0的等比数列,
.
(1)求数列
和
的通项公式;
(2)记
,
,求数列
的前
项和
;
(3)记
,
,证明数列
的前
项和
.
![](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/eeb221d1bf9cda5fc8c97023b482f521.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25c2a5f8ec179b72b201c3c0a670612a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.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)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6520989362ddad9f9d934f7de6b2edf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9928e46511e601913619a427ded84a3.png)
您最近一年使用:0次
2023-01-13更新
|
785次组卷
|
3卷引用:天津市海河中学2022-2023学年高三上学期期末数学试题
10 . 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)设
,求证:数列
的前
项和![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7c5e8cd6e49ca59236075815832f862.png)
(3)求
,其中
;
![](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)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66633ff837f860d61d0807265c5d855d.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/c7c5e8cd6e49ca59236075815832f862.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75ee9e282f9040aab96cf482b17ed0e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9674b56eeb5c0df9868bc3506fd1b44e.png)
您最近一年使用:0次