名校
1 . 在共有2023项的等比数列
中,有等式
成立,类比上述性质,在共有2023项的等差数列
中,相应的有等式______ 成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80eae440bc359521b680637e9401b797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
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23-24高二上·上海·课后作业
2 . 已知在等差数列
中,
.
(1)求证:
对一切小于
的正整数
都成立.
(2)类比上述性质,在等比数列
中,若
,可以得到什么结论?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83dda756cca393b4480163274559fbdd.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a61600b0fc1711f732666ce0198419e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be7581dbbccda50e5d5cd18056ddea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)类比上述性质,在等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab3c7f5b4cf0ac13e8c16aa5b0a2b15.png)
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3 . 在等差数列
中,若
,则有
.相应地,在等比数列
中,若
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95a9fb3484033f9aa2be1068fca1703a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a3fb3c294d69e4cb523c57e2023a0e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7eb5285acd42f923e483603a3296e25.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 已知
为等比数列,
,则有
.若
为等差数列,
,则数列
的类似结论为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f86a8746a583f411fb73c6334eb27b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c20a234aa2d8a58d89951aa9a9ba7486.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2080d53d0d9f9f935f7652b1c88fff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2023-08-13更新
|
35次组卷
|
2卷引用:河南省济源英才学校2022-2023学年高二下学期4月质量检测数学试卷
名校
5 . 在等比数列
中,有
,类比上述性质,在等差数列
中,有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daee95a6789c64c945e5217e818a82c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2023-05-10更新
|
265次组卷
|
3卷引用:四川省成都市蓉城高中联盟2022-2023学年高二下期期中考试文科数学试题
6 . 已知“若
和
均为等差数列,
和
为常数,则
也是等差数列”,类比以上性质,写出若
和
为等比数列,可以得到的结论,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](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/ae7ac6afbc490003ace65655d5768f4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
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7 . 设
是公比为q的等比数列
的前n项积,则数列
,
,
是等比数列且其公比的值是
通过类比推理,可以得到结论:设
是公差为d的等差数列
的前n项和,则数列
,
,
是等差数列,且其公差为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e4758844bf59b27141b61baf26ef3d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95957397a20e052fb65c6faf5b3312f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4430d0eab74bf18da227da4b17336126.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ace3ad09cad0e7ae0c7a410babcbac92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/142bd84f63530e1fdf2cc53ab3a14037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4740344514cb6f1de52d3a2d8c3ee087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/689dacb4d600f8bd7b94dd71dc849f1d.png)
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8 . 在等差数列
中,若
,则
(
),类比等差数列和等比数列的性质,在正项等比数列
中,若
,则可类比推出( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83dda756cca393b4480163274559fbdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53aca2c7653824652b4ba3736c6e0310.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7b235254e2d5db781e866b535d9321d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de5e72acc9563b77a34d99fe085cfc10.png)
A.![]() |
B.![]() |
C.![]() |
D.![]() |
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9 . 在等差数列
中,公差为
,若
,
,则当
时,
取最大值.类比上述性质,在等比数列
中,公比
,若
,
,则当
时( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d8bbb4a09e0ac86bbae46222a90841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e3066990f452db57e7c3894be6d1061.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8042f0193d244577d8af2b090050c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ec5d76db9bd05547932966c9913dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5fe8fecffe2d718a9a346173e5f7e6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ca664b1e82da6f50064a76fe118aa80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29773eda9633545d69f641674d2e455f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88b87541996da243d7f6be7322031f6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764eff906937f9b1fb58e5abfb2eb8a3.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2022-06-30更新
|
90次组卷
|
2卷引用:江西省吉安市2021-2022学年高二下学期期末教学质量检测数学(文)试题
10 . 已知在等差数列
中,若
,则
对于一切小于19的正整数n都成立;类比上述性质,在等比数列
中,若
,则______ ;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83dda756cca393b4480163274559fbdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4933b9d6848dfc08859a98a4117406d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab3c7f5b4cf0ac13e8c16aa5b0a2b15.png)
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