1 . 正项等比数列
满足
,
,
成等差数列,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b6fae41755ecb64ac239a5a2d767354.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2592ac2cb37871244a53ec0cc2ca8335.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3卷引用:天津市南开中学滨海生态城学校2022-2023学年高三上学期11月月考数学试题
解题方法
2 . 在
中,角A,B,C所对的边分别为a,b,c,且
,
,
成等差数列,若
,则b边的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57003e380cf41982c78289db1c4d68fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1110559eaac39a016c95880c08de39f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7933389f3ab945c1f8a7f0ab16f9c3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9be4380bdcef1c542604a6ad61642c0f.png)
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3 . 已知数列
是等差数列,其前n项和为
,
,
;数列
的前n项和为
,
.
(1)求数列
,
的通项公式;
(2)求数列
的前n项和
;
(3)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/f1d0932cb3f8782d61564a3916e48593.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc9dc08571a7c9a77dc85cad5b578942.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/0d89b19520a44e35fc84f7152aa5be2e.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b62bc8bc6d3ee200adcc7a393844814f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15520cf5be7c2685975aac51bc99ac4f.png)
(3)求证;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03f370fafbcb02c8ecba70936c03d70.png)
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解题方法
4 . 设等差数列
的前
项和为
,若
,
,若对任意的
,
恒成立,则实数
的取值范围是______ .
![](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/f6f35fa103e2d4cfb68dc624dc45608d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae5252f557365b8bc67784f0bc38d212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/670d5fc71b49fdb5411b046bb9a81bab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4645e8feff9bc6bce0b4029ecfbb1472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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5 . 若等差数列
的前三项和
,则
等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5170584604571b5e1afd5ece941e2e73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
A.3 | B.4 | C.5 | D.6 |
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3卷引用:天津市部分区2022-2023学年高三上学期期中数学试题
名校
解题方法
6 . 设等差数列
满足
,
,其前
项和为
,若数列
也为等差数列,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
______ ;
的最大值是______ .
![](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/af49bf1e8541675499171c64c4ca99ef.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/832d1e3a06f59a35396aac6e12c5e2ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cd633474e4022e53e42ecdfac6f0512.png)
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名校
7 . 已知正项等差数列
的前
项和为
,若
,则
的值为( )
![](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/29b121fd54236c070f8640b5a0eb3609.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49ebc48c815899940bfd69c92e093508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cccc33f7dd4c335e786b6317c2f41b0.png)
A.3 | B.14 | C.28 | D.42 |
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8 . 设等差数列
的前
项和为
,且
,
.
(1)求数列
的通项公式;
(2)若
,求数列
的前
项积
.
![](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/0232ec48befa61dc6fa11255904eceb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5032706dd285c22e149c675da465d9ac.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e191086446263b7bbbd93613577c42.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)
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2卷引用:天津市军粮城中学2022-2023学年高三上学期期中数学试题
9 . 设{an}是首项为1的等比数列,数列{bn}满足bn=
,已知a1,3a2,9a3成等差数列.
(1)求{an}和{bn}的通项公式;
(2)记Sn和Tn分别为{an}和{bn}的前n项和.证明:Tn<
.
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fa3de6486d375096e5b3b8cfe038a90.png)
(1)求{an}和{bn}的通项公式;
(2)记Sn和Tn分别为{an}和{bn}的前n项和.证明:Tn<
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3abed851f46886fe48f6bc55316faee7.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca4454314dc1b1727f6c31c6ed8a610.png)
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4卷引用:天津市河西区2022-2023学年高三上学期期中数学试题
名校
解题方法
10 . 已知公差不为0的等差数列
的首项为2,且
,
,
成等比数列.
(1)求数列
的通项公式;
(2)令![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed14a3788bf9c61477b5f5344e903347.png)
,求数列
的前n项和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed14a3788bf9c61477b5f5344e903347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5e07bf129b073f37b553fbca100172.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
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