1 . 在正项无穷数列
中,若对任意的
,都存在
,使得
,则称
为
阶等比数列.若
为1阶等比数列,且
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
_________ ;若数列
是2阶等比数列,且
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6016be828be0c8e87f425f3b9437ba1.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209559aca6bf32705588b6a40e0b7320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49f62d620374c35e1d8d90b6f8b6e801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a327da06d8bf19a6f0ce10089cf303d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a9e8b2a0eed594720eb8a65fefd714a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0223546f654f83bb6ebf4bb52e86157.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1bfdf0c734162745dcebe626bc59cc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd4cf909f2febeea7d169459d0cf0bcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6016be828be0c8e87f425f3b9437ba1.png)
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2 . 已知数列
满足
,且
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5ea47801d8340f3d0ccf3153cb8bcb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0382b4a2ab0657d2d6830bb6be2b17b6.png)
A.3 | B.![]() | C.![]() | D.![]() |
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3卷引用:广西壮族自治区桂林市2023-2024学年高二下学期联合检测考试(3月)数学试题
名校
3 . 已知
是公比不为1的等比数列
的前
项和,则“
成等差数列”是“存在不相等的正整数
,使得
成等差数列”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/089f16d8941a9a57c89a25d1f5fc1017.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ae138b4f85019d3faa39b271342adb.png)
A.充分不必要条件 | B.必要不充分条件 |
C.充要条件 | D.既不充分也不必要条件 |
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3卷引用:广西钦州市2024届高三年级第三次教学质量监测 数学
名校
4 . 记数列
的前
项和为
,若
,且
是等比数列
的前三项,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88fa0877ffbcd7a4a631bfd0424b9ad2.png)
_________ .
![](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/3903653955c424d3f6135edc5b47e231.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84f012ac44d919598712e3415cd34345.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd90110345f6d50801d1e20486d9e182.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88fa0877ffbcd7a4a631bfd0424b9ad2.png)
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2024-01-15更新
|
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4卷引用:广西南宁市2023-2024学年高二上学期教学质量调研数学试题
广西南宁市2023-2024学年高二上学期教学质量调研数学试题广东省广州市广雅中学2024届高三上学期第二次调研数学试题山东省烟台爱华高级中学2023-2024学年高二上学期期末模拟数学试题(三)B卷(已下线)4.2 等比数列(第1课时)(十大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
5 . 设
是等差数列,
是各项都为正数的等比数列.且
,
,
,
.
(1)求
,
的通项公式;
(2)设
,求数列
的前
项和
.
![](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/ebaf2a2590bb84d646957f913d78f6dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/431d1949ced5df0568a4c386a6c99ecd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d936e2b8dc747af717d03452795b908f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a674248873dd371d79428dfe6b297483.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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解题方法
6 . 已知①
;②
;③
,在这三个条件中选一个,补充在下面问题中,并给出解答.
设正项等比数列
的前n项和为
,数列
的前n项和为
,________,
,对
都有
成立.
(1)求数列
、
的通项公式;
(2)若数列
的前n项和为
,证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd94be9195f9653041ba0f26af623f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0863cf59114f905e9ad3debc5572792.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ae90518ab352bc6ac957287c05d819.png)
设正项等比数列
![](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/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40b5b1a811ac265c464a2a3b104b7803.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02efa6f1dc514a278597ed9ccfe42127.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560c16e62b5f900bd578ec8c512b5ca1.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52c9237cb0b4acc568d4afb12997186.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87bd7d18f67e90a7c37fad4252e43c9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dc6c64fe67eae6d7628c617433c2620.png)
您最近一年使用:0次
名校
解题方法
7 . 已知等比数列
的公比
,
且
,
,
成等差数列,数列
前
项和为
,且
.
(1)分别求出数列
和
的通项公式;
(2)设
,其中数列
前
项和为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eda6dc559d07bc22c9a0ed1e3a6d01d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/197257e9083b27e1941bbaf58e3f7d67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827b8c9ad738a2c72539a0cc3fc0f229.png)
(1)分别求出数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9221c0c92a526f65533cdc5400767af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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2023-08-02更新
|
495次组卷
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2卷引用:广西示范性高中2022-2023学年高二下学期6月联合调研测试数学试题
解题方法
8 . 已知等比数列
满足
.
(1)求数列
的通项公式;
(2)求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8f56222250b90feef8a052bf5f5f8cd.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0496f142d8ae5acb06e83526eaa3ef87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
名校
9 . 下列说法中,正确的有( )
A.已知![]() ![]() |
B.数列![]() ![]() ![]() ![]() |
C.已知正项等比数列![]() ![]() |
D.已知等差数列![]() ![]() ![]() ![]() |
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2023-07-16更新
|
829次组卷
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4卷引用:广西北海市2022-2023学年高二下学期期末质量检测卷数学试题
名校
解题方法
10 . 已知各项都为正数的等比数列
,满足
,若存在两项
,
,使得
,则
最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48bf2138c305e7d3ab3c2999eec10c60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681ae1522a36768618f7ddaf74abbb7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa45f845bc583ac93363ae117d591fa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/105f3fdeb0d86c8eab54f4e1f4f2bc96.png)
A.2 | B.![]() | C.![]() | D.1 |
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2023-06-26更新
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