解题方法
1 . 记等差数列
的前
项和为
,公差为
,等比数列
的公比为
,已知
,
,
,
.
(1)求
,
的通项公式;
(2)记
,记
的前
项和为
,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/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86fc336b4a83bf6d66c4afcc431597f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385275d29d8c8a7841eaeaa3dfab2cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7413dcc60aeb14d82d11f2e285768a36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a608299299b60110c1d19784e829a5c3.png)
(1)求
![](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/25c2a5f8ec179b72b201c3c0a670612a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.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/8a352d5b7a39605598f401eff873307f.png)
您最近一年使用:0次
2 . 已知等差数列
的前n项的和为
成等差数列,且
成等比数列.
(1)求
的通项公式;
(2)若
,数列
的前n项的和为
,试比较
与
的大小,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/293fe7601035124ac93b15eb0af7b349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea68ba197cb8727562208a44d36e8144.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fba0a7b41a04139c320a73eae4e3cc59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba1b039c186a8c6af77ec151d623c3a3.png)
您最近一年使用:0次
2024-05-04更新
|
352次组卷
|
2卷引用:河北省石家庄一中2023-2024学年高二下学期第一次月考数学试题
解题方法
3 . 已知等差数列满足
,
,数列
满足
,且
.
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23787abf446a4a81bf3c279defad2ec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)将数列
![](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/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bab9264c2e76f4a6ca690ceec31646ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b9a0d7150fb24be3e28ef7f0e18be93.png)
您最近一年使用:0次
4 . 设等比数列
的前
项和为
,数列
为等差数列,且公差
,
.
(1)求数列
的通项公式以及前
项和
;
(2)数列
的前
项和为
,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/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18883593a07bb08511c484b7af2af5b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20379264b0b9a7d5c421bb23a1eb69fc.png)
(1)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)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f089de77d6fb7f086e899274d2f83a69.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/3ef2348f4e1af38c094221f82040337d.png)
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2023-09-21更新
|
938次组卷
|
4卷引用:专题09 数列求和6种常见考法归类(2)
(已下线)专题09 数列求和6种常见考法归类(2)河北省秦皇岛市青龙满族自治县2023届高三联考模拟(三)数学试题重庆市2024届高三上学期9月月度质量检测数学试题(已下线)专题5-3数列求和及综合大题归类-1
名校
解题方法
5 . 已知数列
是等差数列,数列
是正项等比数列,且
,
.
(1)求数列
、数列
的通项公式;
(2)若
,求证:数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/557f6202db1d5fb71ef88c3878e55919.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccfe26b3ab1cd6a93075f24b696b0cef.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d43b5055cb836281d07c1232d17b60c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc1f5d407c0e99344ed5f0f5926c5d22.png)
您最近一年使用:0次
名校
解题方法
6 . 已知数列
为等差数列,
为
的前
项和,
,
.
(1)求数列
的通项公式;
(2)设数列
的前
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/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a0eecb5b800fce9ae10aed86ffee62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/127943cfb7bfdc1c3f5495b1f4f977cb.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设数列
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9928e46511e601913619a427ded84a3.png)
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2023-11-27更新
|
865次组卷
|
2卷引用:黑龙江省牡丹江市第一高级中学2023-2024学年高二上学期1月期末考试数学试题
名校
7 . 设
是等差数列,
是等比数列,且
.
(1)求
与
的通项公式;
(2)设
的前
项和为
,求证:
;
(3)若
,且数列
的前
项和为
,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/6f6eba282321f5d17e3de9b6544e9f6f.png)
(1)求
![](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/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/702b31070b4001b47426d73831e585b5.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc79e006b192782170fdb16384ba5879.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.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/0022c073e919d163032a4f5923e893ef.png)
您最近一年使用:0次
名校
解题方法
8 . 已知数列
的前
项和为
,
,且
.
(1)求
的通项公式;
(2)若
,数列
的前
项和为
,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/d3a216c1a02266ea5bb508b943e51785.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c32bdd71430429aa7748f7d52d4750f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/216876de04325fd250c38c485cbc34b7.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9928e46511e601913619a427ded84a3.png)
您最近一年使用:0次
2024-02-06更新
|
226次组卷
|
3卷引用:安徽省滁州市2023-2024学年高二上学期1月期末联考数学试题
9 . 已知数列
中,
.
(1)求
的值;
(2)证明:数列
是等差数列;
(3)求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394e12390c0d5a3a924446a3e664af9b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(2)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104f53f449b7d4e24100581864e7446d.png)
(3)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
10 . 数列
满足
,
,
.
(1)求
,
;
(2)证明:数列
是等差数列;
(3)若
,求数列
的前n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/18d8e8f821111de8075e5c3dfb22a5d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50feb194b3a7cd2e437e15e0f6e2c3b3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
(2)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d82c65a855b1eed9c43e6829f6c3bffb.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1340250e0dede8fb55687ee453b12050.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2024-02-12更新
|
1102次组卷
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3卷引用:河北省唐山市2023-2024学年高二上学期期末考试数学试题
河北省唐山市2023-2024学年高二上学期期末考试数学试题河北省承德市宽城满族自治县第一中学2023-2024学年高二下学期期初考试数学试卷(已下线)专题02等差数列及其前n项和7种常考题型归类【好题汇编】-备战2023-2024学年高二数学下学期期末真题分类汇编(北师大版2019选择性必修第二册)