名校
解题方法
1 . 已知等差数列
的前n项和
,
,
,
,数列
的前n项和
,
.
(1)证明:
是等比数列,并求
;
(2)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/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b83d73d014a0ca4aff4282228312f55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d8b342e45701057b54207a39c864f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc20ce2f40a29455b9e387099639605b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fc82353331abee0828dee9b38c08f2.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e3f946894e21775f9d2b4219ed627eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52c9237cb0b4acc568d4afb12997186.png)
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解题方法
2 . 在数列
中,
,
,
.
(1)证明
为等比数列;
(2)求
.
![](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/2693734765399876e9e93cdb110231c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe4efd096fc4315c00596bd2b11ef637.png)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9706a4f824b2b72e5816069672ddfc.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
您最近一年使用:0次
名校
解题方法
3 . 已知等比数列
的各项均为正数,且
,
.
(1)求数列
的通项公式;
(2)令
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/004fd1e0773d7a901e58749b85edd577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf1f46ea2f714ca3653b3f9603e3a63.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3d2fa97c9fe093dea300ff9e31decb.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
解题方法
4 . 已知数列
与
满足
,
且
,
,且
.
(1)设
,
,求
,并证明:数列
是等比数列;
(2)设
为
的前n项和,求
.
![](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/9668edd792fc8fa3b36ea97eb97a5f59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e33f55dbea026cc4f5bc9062974d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ff2aa68223dfc02f39d7d10fa005387.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7cb1986891914137aeb155c76dc970c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7936359df4c926b72b48c6fdae55f12d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c88a7ef007c78a93e33bd77c4396626.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b9a0d7150fb24be3e28ef7f0e18be93.png)
您最近一年使用:0次
2020-10-10更新
|
316次组卷
|
5卷引用:专题18 等比数列——2020年高考数学母题题源解密(海南专版)
(已下线)专题18 等比数列——2020年高考数学母题题源解密(海南专版)(已下线)专题18 等比数列——2020年高考数学母题题源解密(山东专版)浙江省五校2020-2021学年高三上学期第一次联考数学试题(已下线)【新东方】杭州新东方高中数学试卷319江苏省无锡市南菁高级中学2020-2021学年高二上学期(强化班)期中数学试题
5 . 已知数列
是各项均为正数的等比数列,且
,
,则数列
的公比为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/188c2fd902ad57934546c85cddccb64e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69039b77f78f6d0bae438010ac332632.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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名校
6 . 设
是等比数列
的前n项和,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6713772588d37a8cea676e36dfb7c87e.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/e3ad03707bf583523192ae11fc27da07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6713772588d37a8cea676e36dfb7c87e.png)
您最近一年使用:0次
2020-10-10更新
|
234次组卷
|
4卷引用:专题18 等比数列——2020年高考数学母题题源解密(海南专版)
(已下线)专题18 等比数列——2020年高考数学母题题源解密(海南专版)(已下线)专题18 等比数列——2020年高考数学母题题源解密(山东专版)贵州省思南中学2021届高三上学期第二次月考数学(理)试题贵州省思南中学2021届高三上学期第二次月考数学(文)试题
7 . 已知等比数列
的公比
,且
,
是
,
的等差中项.
(1)求数列
的通项公式;
(2)证明:
,设
的前
项的和为
,求证:
.
![](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/7d9b03230cbcdbfb2f70cab2a306b717.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44ae2c13c6e6d0fd01e55c72129f337b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca324f309b9cd8cfc99e9c458b5ce59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.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/5a617582d1c65fd37666ab60a532f62d.png)
您最近一年使用:0次
2020-10-02更新
|
1020次组卷
|
8卷引用:专题18 等比数列——2020年高考数学母题题源解密(海南专版)
(已下线)专题18 等比数列——2020年高考数学母题题源解密(海南专版)(已下线)专题18 等比数列——2020年高考数学母题题源解密(山东专版)(已下线)考点41 等比数列及其前n项和-备战2021年新高考数学一轮复习考点一遍过浙江省金色联盟(百校联考)2020-2021学年高三上学期9月联考数学试题(已下线)第四章 数列(章末测试)-2020-2021学年一隅三反系列之高二数学新教材选择性必修第二册(人教A版)(已下线)第四章 数列-2020-2021学年高二数学同步课堂帮帮帮(人教A版2019选择性必修第二册)人教B版(2019) 选修第三册 必杀技 第五章 素养检测(已下线)4.3.2 等比数列的前n项和公式(同步练习)-【一堂好课】2022-2023学年高二数学同步名师重点课堂(人教A版2019选择性必修第二册)
解题方法
8 . 已知正项等比数列
满足
,
.
(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/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cf1055b5cd61b001c0d82718c41f708.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d61626d0af1da5d95c2e28fba0a7d71c.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6abbf32569be76dec2285e05e1db7e16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.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
解题方法
9 . 已知抛物线
:
的焦点为
,
为坐标原点.过点
的直线
与抛物线
交于
,
两点.
(1)若直线
与圆
:
相切,求直线
的方程;
(2)若直线
与
轴的交点为
.且
,
,试探究:
是否为定值?若为定值,求出该定值;若不为定值,试说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4a4f477059ce51042bbdab55a621328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/705ccb242cf2f2d6d07da0eb4e6700d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b3c5bcab86c4481666a84c215b9fe3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
您最近一年使用:0次
2020-09-26更新
|
1915次组卷
|
8卷引用:专题22 圆锥曲线综合——2020年高考数学母题题源解密(海南专版)
(已下线)专题22 圆锥曲线综合——2020年高考数学母题题源解密(海南专版)(已下线)专题22 圆锥曲线综合——2020年高考数学母题题源解密(山东专版)(已下线)专题12 定比点差法及其应用 微点5 定比点差法综合训练西南名师联盟2021届高考实用性文科数学联考卷(二)云南省云天化中学、下关一中2021届高三复习备考联合质量检测卷(二)数学(理)试题云南省云天化中学、下关一中2021届高三复习备考联合质量检测卷(二)数学(文)试题浙江省2021届高三4月份高考数学模拟试题(10)吉林省长春市十一高中2020-2021学年高二下学期第三学程考试数学(理)试题
解题方法
10 . 已知
为坐标原点,椭圆
:
的左右焦点分别为
,
,左右顶点分别为
,
,上下顶点分别为
,
,四边形
的面积为4,四边形
的面积为
.
(1)求椭圆
的标准方程;
(2)若点
,
为椭圆
上的两个动点,
的面积为1.证明:存在定点
,使得
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92e5d91f4f631c580c155eba8c92bda4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e694ed4fd4d76f641a4212908c0aa55a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf73d4aea1f47686f2bee865be7c69c1.png)
您最近一年使用:0次