名校
1 . 已知等差数列
的前
项和为
,且
.
(1)求数列
的通项公式
;
(2)设
,若对一切正整数
,不等式
恒成立,求实数
的取值范围;.
(3)是否存在正整数
,使得
.成等比数列?若存在,求出所有的
;若不存在,说明理由.
![](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/0fce7b028915a4ce6aabf3e7c4e44ffd.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dccd2dd0616ce63e3bb4d9dfe29925dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/659ac35d7184a67920f0b0031eaaa3c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)是否存在正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ad049edd5369dcfb7c2d57a5671472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90a9a1061e7fdf435111ef3cf392f0d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
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名校
解题方法
2 . 数列
满足
,则数列
的前100项和为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3458a17fd8540a519aa4a14725f9bd27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
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13-14高一下·重庆·阶段练习
3 . 将一个等差数列依次写成下表:
第1行:2
第2行:5 8 11
第3行:14 17 20 23 26
………………………………………………
第
行:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30e843a95617ad24ea4e789a0cdc5912.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c82be573157fd2c8068cb000505b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aec8aa05d77a638e99494af9dfc0896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907e338a2cd8381353173126753e2415.png)
………………![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2814549b2e9f30007ab2d811dd9adf9.png)
(其中
表示第
行中的第
个数)
那么第
行的数的和是_________________ .
第1行:2
第2行:5 8 11
第3行:14 17 20 23 26
………………………………………………
第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30e843a95617ad24ea4e789a0cdc5912.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c82be573157fd2c8068cb000505b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aec8aa05d77a638e99494af9dfc0896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907e338a2cd8381353173126753e2415.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/392546a6637cb8faf9f356f4739cd7e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2814549b2e9f30007ab2d811dd9adf9.png)
(其中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee641d39bc70aa40e611fcfc6b78f30b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
那么第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2012·上海徐汇·一模
名校
4 . 如果存在常数
,使得数列
满足:若
是数列
中的一项,则
也是数列
中的一项,称数列
为“兑换数列”,常数
是它的“兑换系数”.
(1)若数列:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00b50284b0058b20b7ae5e63db2e47e7.png)
是“兑换系数”为
的“兑换数列”,求
和
的值;
(2)已知有穷等差数列
的项数是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7e9f86738335a22298559db41037a4.png)
,所有项之和是
,求证:数列
是“兑换数列”,并用
和
表示它的“兑换系数”;
(3)对于一个不小于3项,且各项皆为正整数的递增数列
,是否有可能它既是等比数列,又是“兑换数列”?给出你的结论,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e53f3ed849beaa4b8b2b22baf49055b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(1)若数列:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00b50284b0058b20b7ae5e63db2e47e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12aab2189a2ba339749cdc8b7e96b357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)已知有穷等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7e9f86738335a22298559db41037a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e5d534dadff2c6feaca4060ea972ff3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7e9f86738335a22298559db41037a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(3)对于一个不小于3项,且各项皆为正整数的递增数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
您最近一年使用:0次
2016-12-01更新
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1376次组卷
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3卷引用:2012届上海市徐汇区高三4月学习能力诊断理科数学试卷