11-12高三下·浙江台州·阶段练习
1 . 设等差数列
的首项
为
,前
项和为
.
(Ⅰ) 若
成等比数列,求数列
的通项公式;
(Ⅱ) 证明:
不构成等比数列.
![](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/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(Ⅰ) 若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f8aa010f7105f3ca426c8a34880abd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(Ⅱ) 证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/366e026d1891e349f702f27113e7f1d0.png)
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2 . 已知公差
的等差数列
满足
,且
成等比数列.
(1)求数列
的通项公式
;
(2)数列
满足
,求数列
的前
项的和
;
(3)设
,若数列
是单调递减数列,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/812be9806122241c476ba1db516c4823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2693734765399876e9e93cdb110231c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6143ff1743d17cc9c92f44dbcca18359.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/806904740dfe923b069c7b37dbe74ece.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/08eb71ecf8d733b6932f4680874dbbf3.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3bd108f4a90eb52ef4d701ec9e463d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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解题方法
3 . 已知
的数列
满足
,
,
成公差为1的等差数列,且满足
,
,
成公比为
的等比数列;
的数列
满足
,
,
成公比为
的等比数列,且满足
,
,
成公差为1的等差数列.
(1)求
,
.
(2)证明:当
时,
.
(3)是否存在实数
,使得对任意
,
?若存在,求出所有的
;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/111d1a60e77d0293acdc3ea1c647d892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a7054cf2f1fefdcea1bb11d966cd8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f339d05a6032c0ca8c4187e75d8ae156.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f339d05a6032c0ca8c4187e75d8ae156.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73c0a2ab7198ec8e80904285ca6eb762.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cbbadf02a2855e91a86dedc7a98781a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/306f3c49c9e05cfafadff14fdf90c3f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/965e8beb4ffed1c9cb0110b7e3f580f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8f51bf9165826c40663d01427c24aba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8f51bf9165826c40663d01427c24aba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56c0ec55d00d28d1a877e6ea38d6cd69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e3875830b3121133833a3b45d3407b6.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f6714682274c31a328bf796e235900.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c881b38e5e74dba689507bde6dfa3c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e87d6c4b41cede82adf564ecb513f326.png)
(3)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209559aca6bf32705588b6a40e0b7320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63b6c614a413bd1db7b6de3a8ff7e7d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
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12-13高三上·浙江宁波·阶段练习
4 . 已知等差数列
的公差
大于0,且
是方程
的两根.数列
的前
项和为
,满足
(
)![](https://img.xkw.com/dksih/QBM/2012/2/11/1570730553032704/1570730558488576/STEM/d0f667e7bc874ee08203e4dcdb722c7d.png?resizew=2)
(1)求数列
,
的通项公式;
(2)设数列
的前
项和为
,记
.若
为数列
中的最大项,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd8e16b5cce392a12326fa2f3ee9acd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26ec29f5cc2c855f97158fdedc2cca9.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ddb7976d2bed9bc3a6567bc670640ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://img.xkw.com/dksih/QBM/2012/2/11/1570730553032704/1570730558488576/STEM/d0f667e7bc874ee08203e4dcdb722c7d.png?resizew=2)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设数列
![](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/92dd3c546a617814371851c445915112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb1222e112464ab97a9decaef4f768c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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