1 . 已知数列
满足
,
,求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdc4f2bb2bdd975d176e8a33f3302ef1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86fc336b4a83bf6d66c4afcc431597f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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2 . 在数列
中,
,求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b956d7e8ed92aa826f13bf625bda9082.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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2023高三·全国·专题练习
3 . 已知数列
满足
,首项
,求其通项公式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9247a1be9e14b6cd79a9afa71f78a04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22532e75200d7232e5517a01ba8b36ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
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2023高三·全国·专题练习
4 . 设数列{an}满足8an+1an-16an+1+2an+5=0(n≥1,n∈N*),且a1=1,记
(n≥1).求数列{bn}的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e6e40d0397695e09566b1cef89347f5.png)
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2023高三·全国·专题练习
5 . 已知数列
满足
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c10f1cbc09ac860c04faec31cd11ba9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
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6 . 已知数列
满足
,
,求
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80ef476ca42ce97254cf85958b7fc8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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2023高三·全国·专题练习
7 . 已知数列
满足
,且
,
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad857a74225e9024a12d2ab552b341b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8323901a49cac29afd7d62864f088077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb334e165679c6cb500c994cffa47147.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
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8 . 设数列
满足
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0f3f46c393e76cbeeed8f3bf50cc713.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
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9 . 证明定理1:对
,
,有
(*)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b86707d7c64c9e0643cfe8653842f2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0462d29f5a16c1351ca1174c7c1abed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18083a01ae2b0efdfaeaa30ece42e719.png)
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