1 . 已知公差不为零的等差数列
的前
项和为
,
,
,
,
成等比数列,数列
满足
,
.
(1)求数列
和
通项公式;
(2)求
的值;
(3)证明
![](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/36183db0759eec0e108274d229fcd00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7da2f386b78cdf6489efaa2f5820d3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4462324656c6ba02a63c24f764da0a9.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34b2cb71f16e36b7fc7860d1a775cb52.png)
(3)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cb03e2661d7d77c1ba0bf9bc887c1e0.png)
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3卷引用:天津市河西区2021-2022学年高三上学期期末数学试题
天津市河西区2021-2022学年高三上学期期末数学试题河北省部分重点中学2022届高三下学期期中数学试题(已下线)押全国卷(理科)第17题 解三角形与数列-备战2022年高考数学(理)临考题号押题(全国卷)
名校
解题方法
2 . 已知数列
的前n项和为
,满足:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6daa0f94b44cd18a1bb642f3dd791dff.png)
(1)求证:数列
为等差数列;
(2)若
,令
,数列
的前n项和为
,若不等式
对任意
恒成立,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6daa0f94b44cd18a1bb642f3dd791dff.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1928c254cfada1f75a5cd1e34db5a63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e5fc0b571e6545e133d36af338733b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b60acaba12709e3fc5be8c4ee47ff395.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
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7卷引用:天津市河北区2023届高三二模数学试题
3 . 已知在各项均不相等的等差数列
中,
,且
、
、
成等比数列,数列
中,
,
,
.
(1)求
的通项公式及其前
项和
;
(2)求证:
是等比数列,并求
的通项公式;
(3)设
求数列
的前
项的和
.
![](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/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bbcab0da135650f774f78156d1f61ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b9aa8112c66efc096e04eb7a9b684af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a70b95c53fb6655721e2a8c61f5c2c.png)
(1)求
![](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)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0791fc0d57d2e1b240c01d4c4901dadc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9441abef0ca046aafd4ce2c91b93be1a.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/fbd85b79372dc6e596d465f738c3c300.png)
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5卷引用:天津市滨海新区七所重点学校2022届高三下学期毕业班联考数学试题
天津市滨海新区七所重点学校2022届高三下学期毕业班联考数学试题天津市第三中学2022届高三下学期三模数学试题(已下线)6.4 求和方法(精练)(已下线)专题05 数列 第二讲 数列的求和(解密讲义)(已下线)高二数学开学摸底考01(江苏专用)-2023-2024学年高中下学期开学摸底考试卷
名校
解题方法
4 . 已知公差不为零的等差数列
中,
,且
,
,
成等比数列,
(1)求数列
的通项公式;
(2)数列
满足
,数列
的前
项和为
,若不等式
对一切
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.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/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/285f98db16b34ddcb0204c8e38578639.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.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/39ede4b754c6562f640fcb902762211d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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4卷引用:天津市红桥区2021-2022学年高三上学期期末数学试题
天津市红桥区2021-2022学年高三上学期期末数学试题山东省聊城市第二中学2021-2022学年高三下学期第一次测评数学试题(已下线)思想01 函数与方程思想(讲)--第三篇 思想方法篇-《2022年高考数学二轮复习讲练测(浙江专用)》(已下线)思想02 分类与整合思想(练)--第三篇 思想方法篇-《2022年高考数学二轮复习讲练测(浙江专用)》
5 . 已知等比数列
的各项均为正数,
,
,
成等差数列,且满足
,等差数列数列
的前n项和
,
,
(1)求数列
和
的通项公式;
(2)设
,求数列
的前2n项和.
(3)设
,
,
的前n项和
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c8afb5276cccd088ed7cada99858bff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4774fd0e7fbe540dd8f52c67ac6a0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f136cae0bc90e8f766e2829d26158d57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fdc528cc909a2fa1395c52a68be68a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aa45ba57a920ce722a0e17307601b92.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/64908d9a973390ea32ee49812ca9e884.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/610be94af2348ae802a0b2c23b3b6183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83d76c3eb0a07a827877d7a4dc306211.png)
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6卷引用:天津市静海区四校2021-2022学年高三上学期12月阶段性检测数学试题
天津市静海区四校2021-2022学年高三上学期12月阶段性检测数学试题天津市第四十三中学2022-2023学年高三上学期期末数学试题天津市南仓中学2022-2023学年高三上学期期末数学试题天津市武清区黄花店中学2022-2023学年高三下学期开学测试数学试题(已下线)专题24 等差数列及其前n项和-3(已下线)山东省济南市2022-2023学年高三上学期期中数学试题变式题15-18
2022高三·全国·专题练习
6 . 已知数列
的前
项和为
,且
,数列
是公差不为0的等差数列,且满足
,
是
和
的等比中项.
(1)求数列
和
的通项公式;
(2)求
;
(3)设数列
的通项公式
,求
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b708c8dcb2d66eb2ce0b3718a9cd924a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc9378ff993c04d1f1ae82d88056d64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee4464b3b4eb6e52ee02f095aae84f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cc748c8c4a12c4fedd5db83a63bb4d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ba4098757b9a76a5e272e6b29eb7fd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37f503e0fbd365dfceebff49d0557441.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bc5f248e68d63ec4ce0e7664ee15d0c.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee4464b3b4eb6e52ee02f095aae84f0.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c306b95434f6a7329cdea7fee3d65581.png)
(3)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cca3ebd10a38201939a3694cc95186a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f28bfdb6842b8c111ee1215cb7da439.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c9ef7dc9139bbfa32da474ddc09136f.png)
您最近一年使用:0次
7 . 已知等比数列
的公比
,前3项和是7.等差数列
满足
,
.
(1)求数列
,
的通项公式;
(2)求①
;
②
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d9b6c86435e0ceff94d8ad1cd03737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4995fa0403e013d888c0935ebfe15024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/739ae59f5ecca89bd1c8ea49585a81a8.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea6617945a440d4e01ae41326734163e.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce0fc6c9a3d5a5d40613aa83f1b8c327.png)
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|
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|
2卷引用:天津市和平区2021-2022学年高三上学期期末数学试题
名校
解题方法
8 . 已知等差数列
的前
项和为
,若
,且
,则下列说法中正确的是( )
![](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/fb334e165679c6cb500c994cffa47147.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b46ef93e3029ac9df6353c9df1e996b.png)
A.![]() | B.当且仅当![]() ![]() |
C.不等式![]() ![]() | D.不等式![]() |
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9卷引用:天津市复兴中学2021-2022学年高三上学期第一次月考数学试题
天津市复兴中学2021-2022学年高三上学期第一次月考数学试题黑龙江省大庆铁人中学2021-2022学年高三上学期期中考试理科数学试题黑龙江省大庆铁人中学2021-2022学年高三上学期期中考试文科数学试题(已下线)专题6-1 等差数列,等比数列中性质应用(选填)-1(已下线)专题5 等差数列的单调性和前n项和的最值问题 微点1 等差数列的单调性黑龙江省佳木斯市第八中学2023届高三上学期11月第二次调研数学试题北京市第十七中学2024届高三上学期10月月考数学试题(已下线)第01周周练(4.1数列的概念4.2.1等差数列的概念4.2.2等差数列的前n项和公式)(提高卷)北京交通大学附属中学2021-2022学年高二下学期期中练习数学试题
9 . 已知
为等差数列,
为等比数列,
,
,
.
(1)求
和
的通项公式;
(2)令
,求数列
的前
项和
;
(3)记
.是否存在实数
,使得对任意的
,恒有
?若存在,求出
的取值范围;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebaf2a2590bb84d646957f913d78f6dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74fa54e94c891e9d0a87e693f9e17a4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f061d7de917c07af22bde65907c7d39.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9221c0c92a526f65533cdc5400767af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c88a7ef007c78a93e33bd77c4396626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/050c9501063924ae4f079245d8e9ff40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e72af37873045f7e7b0199e41c1361f.png)
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2卷引用:天津市北辰区2022届高三上学期第一次联考数学试题
2017高二·全国·课后作业
名校
解题方法
10 . 等差数列中,
.
(1)求数列的通项公式;
(2)若
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11卷引用:天津市第二十一中学2023-2024学年高三上学期第一次月考数学试题
天津市第二十一中学2023-2024学年高三上学期第一次月考数学试题(已下线)2.3 等差数列的前n项和—《课时同步君》高中数学人教版 必修5 第二章 数列 2.3 等差数列前n项和甘肃省嘉峪关市等3地2022-2023学年高二上学期期末数学试题黑龙江省鸡西市第十九中学2023-2024学年高二上学期11月期中考试数学试题(已下线)BBWYhjsx1112甘肃省白银市会宁县第四中学2023-2024学年高二上学期第一次月考数学试题(已下线)4.2.3 等差数列的前n项和(8大题型)-【题型分类归纳】2023-2024学年高二数学同步讲与练(苏教版2019选择性必修第一册)内蒙古呼伦贝尔市满洲里远方中学2023-2024学年高二上学期期末考试数学试题(已下线)第03讲 4.2.2等差数列的前 项和公式(1)(已下线)4.2.2 等差数列的前n项和公式(8大题型)精讲-2023-2024学年高二数学题型分类归纳讲与练(人教A版2019选择性必修第二册)