名校
1 . 若数列
:
,
,
,
(
)中
(
)且对任意的
,
恒成立,则称数列
为“
数列”.
(1)若数列1,
,
,7为“
数列”,写出所有可能的
、
;
(2)若“
数列”
:
,
,
,
中,
,
,求
的最大值;
(3)设
为给定的偶数,对所有可能的“
数列”
:
,
,
,
,记
,其中
表示
,
,
,
这s个数中最大的数,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/238d69b84446b56240d2a8ea5de04837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef835c9ad2636a9662fb6c99e3abc78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51502a5f4107db67ec1f1b3fa4a4244f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/920423f1a05fab3a52daf0f3e9e05a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b853c5147ef5cdee4a6f9ad28737f8.png)
(1)若数列1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b853c5147ef5cdee4a6f9ad28737f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(2)若“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b853c5147ef5cdee4a6f9ad28737f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6c2130a7cbbcd1554f4863e1666408d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7e9f86738335a22298559db41037a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b853c5147ef5cdee4a6f9ad28737f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8204e935be0688ce1561d9107b635480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59f2804e8a9db3a0ada6c34972e4342a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b125c9321c0d8bd9cf942d6da8bebf16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/637f94c79ddadc15f305bed8adc45733.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
2017-11-18更新
|
1053次组卷
|
5卷引用:北京市海淀区2018届高三上学期期中考试数学(理)试题
名校
2 . 若数列
满足:对于任意的正整数
,
,
,且
,则称该数列为“跳级数列”.
(1)若数列
为“跳级数列”,且
,求
、
的值;
(2)若数列
为“跳级数列”,则对于任意一个大于
的质数
,在数列
中总有一项是
的倍数;
(3)若
为奇质数,则存在一个“跳级数列”
,使得数列
中每一项都不是
的倍数.
![](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/9adf73921cc2d04b4f23ee9224b7b8fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a5945ce5c2114af8c18718ca8dc899.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06c9c905d2ffd48dc7cc966cd1f0e2e8.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0748c346ed88f98e424de8edf278325.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2344f4d2455e19a0e16f21efd75e9991.png)
(2)若数列
![](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/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.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/b1010846eeec6c9da29640f5aa3f8738.png)
您最近一年使用:0次
2019-12-22更新
|
557次组卷
|
2卷引用:北京市海淀区一零一中学2019-2020学年高三上学期期中数学试题
名校
解题方法
3 . 已知点
在函数
的图象上,数列
的前
项和为
,数列
的前
项和为
,且
是
与
的等差中项.
(1)求数列
的通项公式;
(2)设
,数列
满足
,
.求数列
的前
项和
;
(3)在(2)的条件下,设
是定义在正整数集上的函数,对于任意的正整数
,恒有
成立,且
,
为常数,
),试判断数列
是否为等差数列,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10f65845003249a18c345251b6299172.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f8bbd32b61f51c189fa50005ea78dbc.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/08eb71ecf8d733b6932f4680874dbbf3.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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37353da4aae7b7238a13ec050ea992fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f6b1b0d0c6cc1b15fefad52052b8af5.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/136eeb246eff6409e0cc2ea4055ea1b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff9744323db67a071fc1901ceae79c6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c8d7b28f5984b91abf284d56ffbf7e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66d4e8502106802f1485c3b0f28f2664.png)
(3)在(2)的条件下,设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b084be72be63541b309c6a6be2a35ab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45aa38f18fd345c8e927733e950e2a85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2af172cbe7ad97f0c60da3b66f79323.png)
您最近一年使用:0次
4 . 设数列
的各项均为非零的整数,其前
项和为
.若
为正偶数,均有
,且
,则
的最小值为( )
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a94774a88d80d7c78f103c095f68a152.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44bf235c15687a5a6b68b7c98ac66013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdd3a25ac2cde3d2c884028f750cfff8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3cf6f2bbe20a404fea41a4d2b1c4c7.png)
A.0 | B.22 | C.26 | D.31 |
您最近一年使用:0次