解题方法
1 . 已知
是等差数列
的前
项和,
,数列
是公比大于1的等比数列,且
,
.
(1)求数列
和
的通项公式;
(2)设
,求使
取得最大值时
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4414e88541187aa93beb4b5c2601862c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a539f4656a7ff726f3cd77321bd92744.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e46afd640072fd6a5e2c94bb72c698b.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbf68dfbe8feafc4d6b9218b352ffee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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解题方法
2 . 等比数列
中,
为其前
项和,
,且
成等差数列,则
的最小值为( )
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f24ce436a9b2f3a8154fb5f819a56f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e160c7696ef719dcebdfb241fb4d83dd.png)
A.![]() | B.![]() | C.![]() | D.1 |
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解题方法
3 . 设数列
满足
,若对一切
,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/e052522f33205927e1342821eda30ccf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1d8fed5f93189944210b255338e551.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
4 . 设无穷数列
的通项公式为
.若
是单调递减数列,则
的一个取值为____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac50f8e55b80c137415796235e38efa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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5 . 在数列
中,
,
,
,则
的前n项和
的最大值为______ .
![](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/4ac8419cf6c0e1d70ea5f5a9eb6dad9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b319b134ec6503a782408308deebae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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6 . 已知数列
的前n项和为
,且关于n的不等式
有3个解,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24dee5b99d61861d4925a62be2490825.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e05ba35399687471803cf46f20ffdff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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7 . 已知数列
是首项为
,公比为
的等比数列,且
,则
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c895d4ce5ce82ef9b311b9369b4de11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df6e651c007afce7bfa5d080aee55143.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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名校
解题方法
8 . 已知数列
的通项公式为
,则数列
中的最小项的值为__________ .(用具体数字作答)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8781d32aa0d87eb724d2be7e29806a8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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9 . 南宋数学家杨辉为我国古代数学研究作出了杰出贡献,他的著名研究成果 “杨辉三 角” 记录于其重要著作《详解九章算法》中, 该著作中的 “垛积术” 问题介绍了高 阶等差数列. 以高阶等差数列中的二阶等差数列为例,其特点是从数列中第二项开始,每一项与前一项的差构成等差数列. 若某个二阶等差数列
的前四项分别为:
,则下列说法错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e59eefa7d589908601bc0b2014acd74.png)
A.![]() | B.![]() |
C.数列 ![]() | D.数列 ![]() |
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解题方法
10 . 已知数列
的通项公式为
,前
项积为
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd1185cac997f45b202c8bf9a33d8186.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
A.在数列![]() ![]() | B.在数列![]() ![]() |
C.数列![]() | D.使![]() ![]() |
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