题型:
难度:
1 . 已知数列
是等差数列,数列
是正项等比数列,且
,
,
是和
的等差中项,
是
和
的等比中项.
(1)求数列
和数列
的通项公式;
(2)令
,求数列
的前n项和.
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/034ba25825c13725931c483aa47c9363.png)
![](/uploads/image/squformula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](/uploads/image/squformula/2a0d29f34218cd60cc6e9ce4dcd13925.png)
![](/uploads/image/squformula/b715e7842b95f654f16056a7c7f2abe9.png)
![](/uploads/image/squformula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](/uploads/image/squformula/f65fc200f10b97588a0c9896277c9c64.png)
![](/uploads/image/squformula/b715e7842b95f654f16056a7c7f2abe9.png)
![](/uploads/image/squformula/57483e04fd1840c87ac5325157149877.png)
(1)求数列
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/034ba25825c13725931c483aa47c9363.png)
(2)令
![](/uploads/image/squformula/115f794e70a18315fb41bdbbb599eb5b.png)
![](/uploads/image/squformula/57ef6d44448092ebdb9e4a49d866a749.png)
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1卷引用:广东省东莞市2023-2024学年高二上学期期末教学质量检查数学试题
2 . 已知数列
满足
,
,
数列
,
的前n项和分别为.
(1)求
,并证明数列
为等比数列;
(2)当
时,有恒成立,求正整数m的最小值.
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/b13a6e1d671215fc96e4bee3541d1096.png)
![](/uploads/image/squformula/60d3eaf50c4cacfbe369e12984e8b31a.png)
![](/uploads/image/squformula/a784243ca60ed9fa55480c6987d40605.png)
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/034ba25825c13725931c483aa47c9363.png)
(1)求
![](/uploads/image/squformula/d7de777f1b9ad8ffaf3568c093b2f7c5.png)
![](/uploads/image/squformula/c8194a62bc60a9da9b5cf76f9dc0fa09.png)
(2)当
![](/uploads/image/squformula/856b137a34d2d5b20671b7a3c7a29606.png)
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3 . (1)在等比数列
中,已知,求;
(2)一个等比数列的首项是
,项数是偶数,其奇数项的和为
,偶数项的和为
,求此数列的公比和项数.
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)一个等比数列的首项是
![](/uploads/image/squformula/bdaa19de263700a15fcf213d64a8cd57.png)
![](/uploads/image/squformula/83fd1dadbe1b2cafc0cf8b5bb8b18ed9.png)
![](/uploads/image/squformula/5ca15cd772284da8cf1899d388df3a8c.png)
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1卷引用:第四章 数列(知识归纳 题型突破)-2023-2024学年高二数学单元速记·巧练(苏教版2019选择性必修第一册)
(已下线)第四章 数列(知识归纳 题型突破)-2023-2024学年高二数学单元速记·巧练(苏教版2019选择性必修第一册)
名校
解题方法
4 . 在等比数列
中.
(1)已知
,
,求前4项和
;
(2)已知公比
,前6项和
,求.
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)已知
![](/uploads/image/squformula/2815b24f5a89be7ae53aed93182e8988.png)
![](/uploads/image/squformula/ea432be66a5d2f9c5198ff656b18fd32.png)
![](/uploads/image/squformula/0f30f56664446f32dbbc2c5f12a99374.png)
(2)已知公比
![](/uploads/image/squformula/26d9b6c86435e0ceff94d8ad1cd03737.png)
![](/uploads/image/squformula/a8b7b67a73a815fb9792f0567396a78b.png)
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1卷引用:广西壮族自治区三新学术联盟2023-2024学年高二上学期期末教学质量检测数学试题
名校
解题方法
5 . 已知
是等差数列,其前n项和为
,
,则下列结论一定正确的有( )
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](/uploads/image/squformula/72db14b97a5318c818b61a19862218c2.png)
a. | b.![]() |
c. | d.![]() |
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1卷引用:广西壮族自治区三新学术联盟2023-2024学年高二上学期期末教学质量检测数学试题
6 . 已知数列
是等差数列,满足
,
,数列
是首项为1的等比数列,且
,
,
成等差数列.
(1)求
,
的通项公式;
(2)设
,求数列
的前
项和.
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/be0d1a492ec22f4ca2372e2c59c61d6c.png)
![](/uploads/image/squformula/79b50b3927041221a53f19b6a0549d71.png)
![](/uploads/image/squformula/034ba25825c13725931c483aa47c9363.png)
![](/uploads/image/squformula/d0eeacc31bfbd4c536bb52bbaec43dd3.png)
![](/uploads/image/squformula/1a8aada7b854c906305d0747c33f9929.png)
![](/uploads/image/squformula/57483e04fd1840c87ac5325157149877.png)
(1)求
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/034ba25825c13725931c483aa47c9363.png)
(2)设
![](/uploads/image/squformula/1d44ddab6e0c60119be69985ae7fa65b.png)
![](/uploads/image/squformula/57ef6d44448092ebdb9e4a49d866a749.png)
![](/uploads/image/squformula/b6a24198bd04c29321ae5dc5a28fe421.png)
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7 . 数列
的前
项和为
,
,则![](/uploads/image/squformula/e3f7fda69e2b32b9ced2239f915fa59b.png)
_________ ;设数列
的前
项和为
,则![](/uploads/image/squformula/7978d7bd6f6caf9ac9837ffce5f89654.png)
________ .
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](/uploads/image/squformula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](/uploads/image/squformula/a742ea39d5f4c69ecb789537648bcb4b.png)
![](/uploads/image/squformula/e3f7fda69e2b32b9ced2239f915fa59b.png)
![](/uploads/image/squformula/362832fa3d3c13c1eafd565349d66dce.png)
![](/uploads/image/squformula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](/uploads/image/squformula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](/uploads/image/squformula/7978d7bd6f6caf9ac9837ffce5f89654.png)
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8 . 已知等差数列
的前
项和为
,若
,公差
,则
的最小值为( )
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](/uploads/image/squformula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](/uploads/image/squformula/4ac577f987d768e1a115f2747ec0fd6d.png)
![](/uploads/image/squformula/c5c1344592c925b273f2cb9b9e47ebbb.png)
![](/uploads/image/squformula/08eb71ecf8d733b6932f4680874dbbf3.png)
a.![]() | b.![]() | c.![]() | d.![]() |
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9 . 在等差数列
中,
.
(1)求
的通项公式;
(2)若
,求数列
的前
项和
.
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/0c829f05f89e6ed594393c20e5964a4f.png)
(1)求
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](/uploads/image/squformula/986babee20ac8ba50add7fe442e08173.png)
![](/uploads/image/squformula/034ba25825c13725931c483aa47c9363.png)
![](/uploads/image/squformula/e2d51f9147b8265c0276c1f2c2659197.png)
![](/uploads/image/squformula/3b9a0d7150fb24be3e28ef7f0e18be93.png)
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