1 . 已知数列
满足
,设
.
(1)证明:数列
为等差数列,并求
的通项公式;
(2)求数列
的前
项和
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/150621da3f2afebfd4dd8df7fa7e507e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14f989f6932c4ecdea167da06b89ffd5.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求数列
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2 . 已知数列
满足
,且
.
(1)求证:数列
为等差数列,并求出数列
的通项公式;
(2)若
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8efc00556a20d6d5d63f15318eb8b128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4cecbdebeb5d12fbe1d54b81cc05a8.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/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2021-11-24更新
|
1171次组卷
|
6卷引用:河南省九师联考2021-2022学年高二上学期期中考试文科数学试题
3 . 已知数列
的前
项和为
,且
.
(1)证明:
是等差数列.
(2)求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4555dca34cc0ad25f9648d19bcbb69da.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba57c83d526ac308d1461e80fcca9f36.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
2021-11-24更新
|
993次组卷
|
2卷引用:河南省新乡市2021-2022学年高二上学期期中考试理科数学试题
解题方法
4 . 已知等差数列
的前
项和为
,且
,
,数列
满足
,且
,
.
(1)求数列
,
的通项公式;
(2)设
是否存在
,使得
成立?若存在,求出
的值;若不存在,请说明理由.
![](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/181967fe81f94621cb446130c99c3121.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36989853e0d247e504b292e17d8a8cfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/773477cee2f369d1f5ac386d1b00eca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f42d4e1c8ecb35727dc43510d79fea87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e85bf74453708682ee3de6c1898753e5.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/eae471a33c52147a77e26757c2f114ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f6b18b109a656b62fb173680ae99ca7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44c89cdca7960c8bcb4261ad1ae1cc71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
5 . 若数列
中,
,
,则
的值等于___________ .
![](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/b478a7aafe8e29a8daac0384f13794b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e35eeaabd951fb09b2926807da3685b.png)
您最近一年使用:0次
解题方法
6 . 已知正项数列
的前
项和为
,且
,
,数列
满足
,
.
(1)求证
为等差数列;
(2)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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b494faa6c15c829953ed56252d3817a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385275d29d8c8a7841eaeaa3dfab2cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/414a642d33ebbba41074018a1d6aa8ee.png)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7feb7cba4c5a54e592e7aae51016bac.png)
您最近一年使用:0次
名校
7 . 已知数列
中,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56c6ce06c1cd6542d0bb2bedaf66b8cf.png)
________ .
![](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/3d46e527415401665298f12bf1a5ef52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56c6ce06c1cd6542d0bb2bedaf66b8cf.png)
您最近一年使用:0次
2020-12-03更新
|
619次组卷
|
3卷引用:河南省开封市2020-2021学年高二上学期五县联考期中数学(文)试题
解题方法
8 . 已知数列
满足
,
.
(1)判断数列
是否为等差数列,并说明理由;
(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/877f3a4e38514cf1b74f9a2422b8deca.png)
(1)判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d952560a646941e247b251071ec26e86.png)
(2)求数列
![](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)
您最近一年使用:0次
9 . 已知数列
满足
,
,设
.
(1)求证数列
为等差数列,并求
的通项公式;
(2)若
,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/c224ee3a4d9f857aa6e115ef5a91e02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/980d51ba3340a31964fbec9e6f243ca6.png)
(1)求证数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3dbefc15ac3ebea7d6c7db14fce2b60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2020-10-18更新
|
742次组卷
|
2卷引用:河南省郑州外国语学校2020-2021学年第一学期高二期中数学(文科)考试试题
10 . 在数列
中,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923c8b51ec77be2d2f41407419ba15f3.png)
(1)求
,猜想数列
的通项公式;
(2)证明:数列
是等差数列.
![](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/923c8b51ec77be2d2f41407419ba15f3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed529240a883f68f0921e818addeb9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7b78e4a03d4595f14be42054b61dfc6.png)
您最近一年使用:0次
2020-06-17更新
|
577次组卷
|
4卷引用:河南省洛阳市2019-2020学年高二下学期期中考试数学 (文)试题
河南省洛阳市2019-2020学年高二下学期期中考试数学 (文)试题河南省信阳市2021-2022学年高二下学期期中教学质量检测数学(文科)试题(已下线)专题27 等差数列与等比数列问题的精彩妙解-备战2022年高考数学一轮复习一网打尽之重点难点突破(已下线)专题12 盘点等差(比)数列的判断与证明——备战2022年高考数学二轮复习常考点专题突破