10-11高三·安徽合肥·阶段练习
名校
解题方法
1 . 已知抛物线
,过点
的直线
与抛物线交于
、
两点,且直线
与
轴交于点
.(1)求证:
,
,
成等比数列;
(2)设
,
,试问
是否为定值,若是,求出此定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25ce60648ea5042ab5eb5702efe651a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4ece5cea3875ab679f56561e9d2d6ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f6d22b25657d8caef12bf302d64dc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/687c1669a54820dd40380d32aed3a476.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/599e26e7cfebd1b4da83a1a5c2cc6b47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05095cd3e70d6e3b1b519309c697d7d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e197143a3210c70f87d5147128e80de.png)
您最近一年使用:0次
2019-01-30更新
|
441次组卷
|
7卷引用:吉林省长春市文理高中2022-2023学年高二上学期期末数学试题
吉林省长春市文理高中2022-2023学年高二上学期期末数学试题(已下线)2011届安徽省合肥市高三第一次教学质置检测理科数学卷(已下线)2011-2012学年湖北襄阳四中、荆州、龙泉中学高二下期中理科数学(已下线)2011-2012学年山东冠县武训高中高二下第二次模块考试理科数学试卷2015届黑龙江省哈尔滨九中高三第三次高考模拟理科数学试卷2015届黑龙江省哈尔滨九中高三第三次高考模拟文科数学试卷黑龙江省牡丹江市第一高级中学2019-2020学年高二上学期10月月考数学(文)试题
2 . 已知数列
满足
,
,
.
(1)证明:数列
为等比数列;
(2)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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d6bf8a38c9288b535c223516360cd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f1179414a71459a3cfa134ace94302e.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2019-06-18更新
|
4751次组卷
|
25卷引用:吉林省松原市宁江区实验高级中学2018-2019学年高二下学期期末考试数学(文)试题
吉林省松原市宁江区实验高级中学2018-2019学年高二下学期期末考试数学(文)试题吉林省松原市宁江区实验高级中学2018-2019学年高二下学期期末数学(理)试题2019年吉林省延吉市延边第二中学高三上学期第一次调研数学(文)试题【省级重点学校】安徽省定远中学2019届高三全国高考猜题预测卷一数学(文)试题(已下线)第03讲 等比数列及其前n项和(讲)-《2020年高考一轮复习讲练测》(浙江版)(已下线)2019年9月22日 《每日一题》2020年高考理数一轮复习-每周一测江西省赣州市十五县市2019-2020学年高三上学期期中数学(文)试题(已下线)专题6.4 等差、等比数列与数列求和(练)【理】-《2020年高考一轮复习讲练测》(已下线)2020届高三3月第01期(考点06)(理科)-《新题速递·数学》(已下线)2020届高三3月第01期(考点06)(文科)-《新题速递·数学》2020届山东省淄博市部分学校高三下学期3月教学质量检测数学试题九师联盟2018-2019学年高三押题信息卷数学文科(一)2020届陕西省高三第三次联考文科数学试题山东省2020届普通高等学校招生全国统一考试数学试题模拟卷(三)(已下线)第7篇——数列-新高考山东专题汇编(已下线)专题7.3 等比数列及其前n项和(精练)-2021年新高考数学一轮复习学与练江西省赣州市十五县(市)2021届高三上学期期中联考数学(文) 试题(已下线)专题7.3 等比数列及其前n项和(讲)-2021年新高考数学一轮复习讲练测河南省郑州市2020-2021学年度上学期高三二调考试数学文科试题福建省“永安一中、德化一中、漳平一中”2021届高三12月三校联考数学试题江苏省南通市平潮高级高中2020-2021学年高二上学期10月学情检测数学试题2019年黑龙江省大庆实验中学高三上学期开学考试数学(文)试题广东省佛山市顺德区第一中学2021-2022学年高二下学期期中数学试题福建省永泰县第一中学2023届高三上学期10月月考数学试题陕西省渭南市白水县2021-2022学年高二上学期期末理科数学试题
名校
解题方法
3 . 设数列
的首项
,且
,
,
.
(1)证明:
是等比数列;
(2)若
,数列
中是否存在连续三项成等差数列?若存在,写出这三项,若不存在说明理由.
(3)若
是递增数列,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f258934739ab0989ebaa00025abcdfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6449976ac45703bf448dd960f0c315c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/225194b4c3de347ddf755be14b4bce90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2889dd3096379db5dfdd51305bdbb743.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40f4e1236d7dc0366d9523d0cbb426be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
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2018-11-10更新
|
832次组卷
|
6卷引用:吉林省长春市农安县农安高级中学2022-2023学年高二下学期4月月考数学试题
名校
4 . 已知数列
的前
项和为
,且满足
.
(1)求数列
的通项公式;
(2)令
,记数列
的前
项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/944cb4ab12bd0f9c45fc69d662b7fa9a.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0f6000421c5370e4b89f23be199f388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfccc89f83f2af31049391057c8f525d.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/f1cb91e89800a81f4d62ed75c3ace24a.png)
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2018-10-04更新
|
1503次组卷
|
3卷引用: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
5 . 已知数列
的前
项和为
,且
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
(1)证明:
是等比数列;
(2)求数列
的通项公式,并求出n为何值时,
取得最小值,并说明理由.
(
)
![](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/525c088691a59223dc090ca5089bdf6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c895d4ce5ce82ef9b311b9369b4de11.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f3b91f2fa7598843dd34b4dea6b439a.png)
您最近一年使用:0次
6 . 已知Sn是数列{an}的前n项和,a1=4,an=2n+1(n≥2).
(1)证明:当n≥2时,Sn=an+n2;
(2)若等比数列{bn}的前两项分别为S2,S5,求{bn}的前n项和Tn.
(1)证明:当n≥2时,Sn=an+n2;
(2)若等比数列{bn}的前两项分别为S2,S5,求{bn}的前n项和Tn.
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7 .
等差数列
的前
项和为
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d869b202733c43df36075af3732515.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32b6877ef38ec149100206854cff21f6.png)
(1)求
以及![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)设
,证明数列
中不存在不同的三项成等比数列
等差数列
![](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/56d869b202733c43df36075af3732515.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32b6877ef38ec149100206854cff21f6.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c4867dfd2b1fa71e386275fe0fed234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
您最近一年使用:0次
名校
8 . 在等比数列
中,
.
(1)求
的通项公式;
(2)设
,数列
的前
项和
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76eedb8b626a77f8c26d2995bb37067c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea025149c457a3d5c6e508c82f7907f.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/94351ce858fa3f3a09cfadc2d23d7253.png)
您最近一年使用:0次
名校
解题方法
9 . 已知数列
满足:
,
.
(
)求
,
,
的值.
(
)求证:数列
是等比数列.
(
)令
,如果对任意
,都有
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/481870593d2c656f975e61da16eaa014.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52e12bd47ed7eaf889dee4c1204408c.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.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/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c895d4ce5ce82ef9b311b9369b4de11.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53ea5b625018a40693daadd75b0e0899.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd624bda9f45309816fc1e6f27e42675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2018-04-02更新
|
699次组卷
|
5卷引用:吉林省长春实验中学2020-2021学年高二上学期开学考试数学试题
名校
10 . 已知
,设
是单调递减的等比数列
的前
项和,
且
成等差数列.
(1)求数列
的通项公式;
(2)记数列
的前
项和为
,求证:对于任意正整数
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.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/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e293fc202a5479d7b2fd0447f386240.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0496f142d8ae5acb06e83526eaa3ef87.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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3853475e5d5310e0b325de06c55116c9.png)
您最近一年使用:0次
2017-12-08更新
|
803次组卷
|
2卷引用:吉林省梅河口市第五中学2017-2018学年高二上学期中期考试数学(理)试题