名校
1 . 已知在平面直角坐标系中,
,
(
),其中数列
、
都是递增数列.
(1)若
,
,判断直线
与
是否平行;
(2)若数列
、
都是正项等差数列,它们的公差分别为
、
,设四边形
的面积为
(
),求证:
也是等差数列;
(3)若
,
(
),
,记直线
的斜率为
,数列
前8项依次递减,求满足条件的数列
的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a42fdaa4763fc6834ed12d4f780c74c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5010b2e9175fdc6fbf5bf88541421d27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ff1c33b81ac2f065d37faef37504bb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81496535a302e25c366e3ffa46e0c54b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc34876d748f30fa4fc2eb6a686b5ff5.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5edf900c810371fb21297c15f86d8743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31ac1def558351e2e3ed1235c570530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0f2a8097208d996bf69f9b0795b0e56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cce224c28ca451c4f105dc3b077736cb.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e4b5779873cb3f4366dbfdb983dec81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f8d1dcfab8e4079c100653603acf75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b741df7d2e8cd077989e4e5401c7d1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef3241705cd0b7fae09b96df8b3e9af6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374cb268ffa23fc0bf12c6e6dc873c4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bbbf4d763f3cbe5a71707bc19c78191.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b311784db139326c27b72a3d55e29c31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
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