2018高三·全国·专题练习
1 . 已知
是等差数列,
是各项均为正数的等比数列,且
,
,
.
(
)求
,
的通项公式.
(
)求数列
中满足
的所有项的和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee4464b3b4eb6e52ee02f095aae84f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c863467a450eeec727b50c55fcec33d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d3d4d3766f714e7b9307395f31b584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/493ddb56c2da01bfe06c62a40322eae4.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee4464b3b4eb6e52ee02f095aae84f0.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c664e225b8d22a2c429857ed57685b.png)
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2 . 数列
,定义
为数列
的一阶差分数列,其中
,(
),设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
(1)若
,求证:
是等比数列,并求出
的通项公式;
(2)若
,又数列
满足:
:
①求数列
的前
和
;
②求证:数列
中的任意一项总可以表示成该数列中其他两项之积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51ee283b481e10694e0cd1f95a32417a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bcd3251fb38a6ff6c858c25a8bcf218.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57cd6a37deca13973355339cc8d122d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ca88e8f6f448c1219554cd23a8da92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55317261005b5a6d0ee3cab9b36469c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78e452f953a94bd2e8a5e3c22dbcbe85.png)
①求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
②求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
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