名校
1 . 解方程或不等式
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9c3a62a60d6980ce31614850fdeb0f4.png)
(2)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c39832874059a4eba9897f2f1e741fa7.png)
(3)求不等式组
的最大整数解.
(4)解关于
的分式方程
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9c3a62a60d6980ce31614850fdeb0f4.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c39832874059a4eba9897f2f1e741fa7.png)
(3)求不等式组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea34731ab35d0b4a20ece917d4095028.png)
(4)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3ae53c2c99b654c95e87623fc75eab4.png)
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2 . 解下列各题:
(1)解方程:
.
(2)求等比数列2,4,8,16,…前十项的和.
(1)解方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f53fd9d1dccf6b20066df5493b5698.png)
(2)求等比数列2,4,8,16,…前十项的和.
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解题方法
3 . 设数列
的前
项和为
,且满足
.
(1)求数列
的通项公式;
(2)解关于
的不等式:
;
(3)若
,求证:数列
前
项和小于
.
![](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/8e7914fdb68e1fbebc44e675e041e5a7.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/082beb2f300cd6d28d2fbbc0709ec26f.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135a6e44401b3e7b21fa1ad1442997fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/478232c9a6b2db6020612a13afb350a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
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名校
解题方法
4 . 已知等差数列
的首项
,公差
,且
,设关于x的不等式
的解集中整数的个数为
.
(1)求数列
的前n项和为
;
(2)若数列满足
,求数列
的通项公式.
![](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/c4ce64685821c3e55c07f151996ca8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d3de6d314dd71900dc8020bb8ab0362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e45a6bd8de1e37fc3d7f21aac8557e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)若数列满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc704a8c18973da608f429452d60a279.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
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2024-04-08更新
|
376次组卷
|
2卷引用:四川省绵阳中学2024届高三高考适应性考试(一)数学(理科)试题
解题方法
5 . 设数列
的前n项和为
,且满足
.
(1)求数列
的通项公式;
(2)解关于n的不等式:
.
![](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/642e798608dc8e2d34948aec80798b5c.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)解关于n的不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d2e0e676c869dea6a14a5c97fe5d3ca.png)
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名校
解题方法
6 . 设数列
的前n项和为
,
,
是公差为1的等差数列.
(1)求
的通项公式;
(2)记
,解关于n的不等式
.
![](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/c5b0da4fcbf9ec484dd9444a18609065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/832d1e3a06f59a35396aac6e12c5e2ee.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/216876de04325fd250c38c485cbc34b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bfbb16b9c05204eff7f0ad025c0c466.png)
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7 . 已知函数
的图象过点
和
.
(1)求函数
的解析式;
(2)记
,
是正整数,
是数列
的前
项和,解关于
的不等式
;
(3)对于(2)中的
,
,整数35是否为数列
中的项?若是求出相应的项数;若不是则说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2042d7826dd3bd564bb45c890d54471e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22239b64da889bde7b92a94743869239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49a31f8e8dba418bd5d886998ef8d17.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d5c2b25051d70362949f4bcbc379fca.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/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcccef9904b053abcf0174b2b9aad807.png)
(3)对于(2)中的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/843258347f85ab71ddf22d4437bbcfa3.png)
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真题
8 . 已知函数
的图像过点
和
.
(1)求函数
的解析式;
(2)记
,
是正整数,
是数列
的前
项和,解关于
的不等式
;
(3)对于(2)中的
与
,整数96是否为数列
中的项?若是,则求出相应的项数;若不是,则说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69c38ae07d077b9c1d50e04955c1b4fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/924507a7b11e6ac2ba1af522ed0dad4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/670f050f37e6c929cba66bd41c3de4d3.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa424430a2256f309701a6f5777bf3e6.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/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcccef9904b053abcf0174b2b9aad807.png)
(3)对于(2)中的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/843258347f85ab71ddf22d4437bbcfa3.png)
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名校
解题方法
9 . 已知
是等差数列,
是等比数列,
.
(1)求
的通项公式;
(2)求数列
的前
项和
,并求不等式
解的最大值.
![](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/b915c46cbc73bc152844f6f03ca075ba.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52c9237cb0b4acc568d4afb12997186.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/5737f1f9cad2471f3ca53241b25a1eb9.png)
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解题方法
10 . 已知数列
满足
.
(1)求证:数列
是等差数列,并求数列
的通项公式;
(2)若
,数列
的前
项和为
,则关于正整数
的不等式
(其中
)最多有几个解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2279dad9128614e32e1b3446fbf336b7.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a44cfbb86a4eb76261c00ddc6bff181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0857559ed421cc7c614708f34f9f3324.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ebc391558f07f7f484df93950fc6cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b8e5990ef4ef314941a3154457a9d4.png)
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