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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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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解题方法
3 . 已知数列
的前n项和为
,若数列为等差数列,且
.
(1)求数列
的通项公式;
(2)若
,求数列
的前n项和
.
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](/uploads/image/squformula/c6a39ae43c737452702d1d0d52dcc37b.png)
(1)求数列
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](/uploads/image/squformula/b1b419a5c728ab4f50d57fb83c7262a2.png)
![](/uploads/image/squformula/034ba25825c13725931c483aa47c9363.png)
![](/uploads/image/squformula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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4 . 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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5 . 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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解题方法
6 . 已知
为数列
的前
项和,满足
,数列
是等差数列,且
.
(1)求数列
和
的通项公式;
(2)求数列
的前
项和.
![](/uploads/image/squformula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](/uploads/image/squformula/f985ba3b26e98eff61d15c39e627fa21.png)
![](/uploads/image/squformula/034ba25825c13725931c483aa47c9363.png)
![](/uploads/image/squformula/74cddbec05eb7aecc2f229f5fdf9c8dd.png)
(1)求数列
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/034ba25825c13725931c483aa47c9363.png)
(2)求数列
![](/uploads/image/squformula/5344eadd4711db34e3f935aedd5fb270.png)
![](/uploads/image/squformula/b6a24198bd04c29321ae5dc5a28fe421.png)
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7 . 已知数列
的通项公式为
,数列
的通项公式为
,
为正整数,若数列
中去掉
的项后,余下的项按原顺序组成数列
,则![](/uploads/image/squformula/58df886060a866eeeddb6b666a0e680b.png)
______ .
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/e21a2abecb477ad5ff15db0f3d7817f3.png)
![](/uploads/image/squformula/034ba25825c13725931c483aa47c9363.png)
![](/uploads/image/squformula/15ff259bff098430a6512d0e4f6fb2d9.png)
![](/uploads/image/squformula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](/uploads/image/squformula/034ba25825c13725931c483aa47c9363.png)
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/57ef6d44448092ebdb9e4a49d866a749.png)
![](/uploads/image/squformula/58df886060a866eeeddb6b666a0e680b.png)
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解题方法
8 . 设数列
满足
,
,
.
(1)证明:数列
为等比数列;
(2)求数列
的通项公式.
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](/uploads/image/squformula/9c9b6e51986fe5d7a7265e0e93adcb4d.png)
![](/uploads/image/squformula/aec696e34e5b6c3173021b21ec1b00e3.png)
(1)证明:数列
![](/uploads/image/squformula/63b1d7e0e5a83289e4a0b745faf0627d.png)
(2)求数列
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
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9 . 已知数列
是各项为正数的数列,前n项和记为
,
,(
),
(1)求数列
的通项公式;
(2)设
,
,求数列
的前n项和
.
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](/uploads/image/squformula/16789712fe64778f607d9d84a9094b54.png)
![](/uploads/image/squformula/e97769855336d73371930df1f187875e.png)
(1)求数列
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](/uploads/image/squformula/adefc7f406cfc667c0f8f51348d5febc.png)
![](/uploads/image/squformula/e97769855336d73371930df1f187875e.png)
![](/uploads/image/squformula/034ba25825c13725931c483aa47c9363.png)
![](/uploads/image/squformula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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1卷引用:山西省晋城市第一中学校2023-2024学年高三上学期第十二次调研考试数学试题
10 . 已知数列
的前
项和为
,
,且满足
.
(1)求数列
的通项公式;
(2)设
,求数列
的前
项和
.
![](/uploads/image/squformula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](/uploads/image/squformula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](/uploads/image/squformula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](/uploads/image/squformula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](/uploads/image/squformula/fe6bd1ac36bdf5fcc61451877c397d8b.png)
(1)求数列
![](/uploads/image/squformula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(2)设
![](/uploads/image/squformula/9b3abd8f6a98fb643e1ec0761a60e650.png)
![](/uploads/image/squformula/0f329b217e1051b23f0d61023cdc6e69.png)
![](/uploads/image/squformula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](/uploads/image/squformula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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