名校
1 . 等差数列
的公差d≠0,a3是a2,a5的等比中项,已知数列a2,a4,
,
,……,
,……为等比数列,数列
的前n项和记为Tn,则2Tn+9=_______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29518f13a1ebc3fff8181c2d7cfba22f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f049f317a9217026eb802c8d461bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caab6829e4599366a283cd60a21d13e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/664d578479b92a2ad0dde097ad502da7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf7709b35b14c00e3d8b5f26f1e070b6.png)
您最近一年使用:0次
解题方法
2 . 设数列
的首项为1,前n项和为
,若对任意的
,均有
(k是常数且
)成立,则称数列
为“
数列”.
(1)若数列
为“
数列”,求数列
的通项公式;
(2)是否存在数列
既是“
数列”,也是“
数列”?若存在,求出符合条件的数列
的通项公式及对应的k的值;若不存在,请说明理由;
(3)若数列
为“
数列”,
,设
,证明:
.
![](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/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2002a484aeb332ebd6d4d78d4abe5b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf5776ec7059c208daf01ca48a34915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daac43c7675fa411b35028e09b0bad90.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2387880727d458702651d699e76d7d76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)是否存在数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daac43c7675fa411b35028e09b0bad90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365bd7d058ae516237811aa0d24d9562.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a5d8bc28ee110a9540f383828b7d245.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9b6e51986fe5d7a7265e0e93adcb4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fc48cdb0d965c38b8765599ee90c299.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3819480e1e624208f729ad8653e4f24f.png)
您最近一年使用:0次
2018-03-06更新
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1868次组卷
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6卷引用:江苏省南京师范大学附属中学、天一、海门、淮阴四校2018届高三联考数学调研测试试题
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