名校
解题方法
1 . 已知各项均不为0的等差数列
的前n项和为
,若
,且
成等比数列.
(1)求数列
的通项公式与
;
(2)设
,数列
的前n项和为
,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/89b24e22503480d88ec847c9bc1be5d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d9440ce7a1f5a748a19b16d5fca4fd8.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a27c2ba5c88efc0212579db055b053e8.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/c215db1d8f69757118ad405b78035628.png)
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2022-11-22更新
|
327次组卷
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3卷引用:天津市武清区城关中学2023-2024学年高三上学期第一次阶段性练习数学试题
2 . 已知正项等差数列
与等比数列
满足
,
,且
既是
和
的等差中项,又是其等比中项.
(1)求数列
和
的通项公式;
(2)记
,其中
,求数列
的前2n项和
;
(3)令
,求证
.
![](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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eab7d59ce066c8f0b346719003f8e28f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea74a5cf39bd1149aed1ce6c8ba0c895.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/161a7b35d1812e6745ae7f7c540cf87a.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/48ab19d5a8c560c50f98d3c740cdcce5.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/3b9a0d7150fb24be3e28ef7f0e18be93.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf2443287aedee2d3385a27b101cbfd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89e491daeb7795dcdf667cdef82a0200.png)
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2022-04-29更新
|
726次组卷
|
3卷引用:天津市滨海新区塘沽第一中学2022届高三下学期4月统练数学试题
名校
解题方法
3 . 已知数列
是等差数列,公差
,
,其前
项为
(
).且
成等比数列.
(1)求数列
的通项
及前
项和
;
(2)若
,数列
的前n项和为
,证明:对
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ce64685821c3e55c07f151996ca8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.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/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6138d9141850a9e9984588faca92d3c3.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10a1940a3544f510311ef4836f955108.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1815037f42fb013f351390a718e37cfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b401c8b49663dcbddbcf372c6c31720b.png)
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4 . 成等差数列的三个正数的和等于15,并且这三个数分别加上2、5、13后成为等比数列{bn}中的b3、b4、b5.
(Ⅰ)求数列{bn}的通项公式;
(Ⅱ)数列{bn}的前n项和为Sn,求证:数列{Sn+
}是等比数列.
(Ⅰ)求数列{bn}的通项公式;
(Ⅱ)数列{bn}的前n项和为Sn,求证:数列{Sn+
![](https://img.xkw.com/dksih/QBM/2017/1/6/1619444287930368/1619444288266240/STEM/fb869952a2da4844bbb954ac11b6da73.png)
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2016-12-03更新
|
2750次组卷
|
12卷引用:天津市河西区2023-2024学年高二上学期期末质量调查数学试卷
(已下线)天津市河西区2023-2024学年高二上学期期末质量调查数学试卷2013-2014学年湖北武汉蔡甸区第二中学高一下六科竞赛理科数学试卷2013-2014学年湖北武汉蔡甸区第二中学高一下六科竞赛数学文试卷2011年普通高等学校招生全国统一考试文科数学(湖北卷)2016-2017学年湖北宜昌葛洲坝中学高二文上期中数学试卷2016-2017学年河南省濮阳市高二上学期期末考试数学(理)试卷2016-2017学年河南省濮阳市高二上学期期末考试(A卷))理数试卷安徽省滁州市定远县育才学校2017-2018学年高一(普通班)下学期第三次月考数学试题【全国校级联考】贵州铜仁伟才学校2017-2018学年高一3月份月考数学试题云南省普洱市景东彝族自治县第一中学2019-2020学年高二下学期期中考试数学(理科)试题2016-2017学年河南省濮阳市高二上学期期末考试(A卷)文数试卷2016-2017学年河南省濮阳市高二上学期期末考试数学(文)试卷
真题
5 . 在数列
与
中,
,数列
的前
项和
满足
,
为
与
的等比中项,
.
(Ⅰ)求
的值;
(Ⅱ)求数列
与
的通项公式;
(Ⅲ)设
.证明
.
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/813be1cf542c45798e71fdc7ba882344.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/0b1f298ceb954a558ea1f4fad3f29af0.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/548ebffc86384a838d27814ae64fc871.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/813be1cf542c45798e71fdc7ba882344.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/a38d1b920aec483c96206d43eee90ac4.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/7a676c7243304dfdb9036b8769b2a157.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/1d0f16dc5a4f41d3adf5f484b898c9f2.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/be312a87633e46cf81335e2fc434e3db.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/b864f3e861b5427aa2be157dbb8a4e60.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/4348208411b44f8189ae0182150f73a9.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/c70e00a82c7a45f09ba87c7ab1646276.png)
(Ⅰ)求
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/e9b838c4e6534ea69e1262eb353cf9af.png)
(Ⅱ)求数列
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/813be1cf542c45798e71fdc7ba882344.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/0b1f298ceb954a558ea1f4fad3f29af0.png)
(Ⅲ)设
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/e32a4e148ded498aa8086a9b5eff70e9.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/fc145be6d0fe45cba96e4235a4dc4739.png)
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