名校
1 . 设等比数列
的公比为q,其前n项和为
,前n项积为
,且满足条件
,
,
,则下列选项正确的是( )
![](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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8141d87fb02b08c88b0c9f27f839a7d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf8fdb1f0fed2d2636c3890b33a8a886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a747534133dc9809cb883728fa59612d.png)
A.![]() | B.![]() |
C.![]() ![]() | D.![]() |
您最近一年使用:0次
2024-02-28更新
|
649次组卷
|
2卷引用:河北省石家庄二中2023-2024学年高二上学期期末数学试题
解题方法
2 . 已知数列
的首项
,且满足
.
(1)求证:
是等比数列,并求出
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/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55ec04d3e591aefb3e110fa1b307aa87.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e1c06829bf8a351bf0d2d29d2889f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37c8395d8d67b07db54304193d7e3004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/801f8d228641b21bd523718fd6738823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
名校
3 . 已知等比数列
中
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ab14dce082f855d0ec4e39ad1304fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdfe37d536c2f83b8da9810fd410f82e.png)
A.10 | B.14 | C.18 | D.54 |
您最近一年使用:0次
名校
解题方法
4 . 若等比数列
的第2项和第6项分别为3和12,则
的第4项为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
A.4 | B.![]() | C.6 | D.![]() |
您最近一年使用:0次
解题方法
5 . 已知等比数列
的前
项和为
,
,且
,
,
成等差数列.
(1)求数列
的通项公式;
(2)已知
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.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/85f7519e1b1dd927bc634eedafc88820.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4b32aee86109b777671cd62868db3b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86e2e42b4aa93db9241103e7f61766c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4afc0af2902e226cd3cb15a4b3343c01.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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
6 . 在等比数列
中,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42e4487468ab2823d6dbf7f0ebd2eb38.png)
________ ;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f966272f7781790ff27e40db6b525253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f26610e8d44f6a4ad1fce0caeb84037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42e4487468ab2823d6dbf7f0ebd2eb38.png)
您最近一年使用:0次
名校
7 . 等比数列
中
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7468cb24657a92735833378a8da3f98e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afd21f4cb498101d26b4aaa2e1a6addc.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
8 . 已知首项为1的正项等比数列
满足
.
(1)求
.
(2)令
,
是数列
的前
项和,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d625d94a59c9c95533fb79e908bc275.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb78d3a4209ebbede94346ba8cfc997a.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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8050391385b496e9c059201e4f12600a.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 . 已知等比数列
的前
项和为
,若关于
的不等式
恒成立,则实数
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de83efe136c57fa34d895f2c335ed95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/696fbd9c72a245e0173bdcdb16e2064c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
A.9 | B.18 | C.27 | D.54 |
您最近一年使用:0次
10 . 侏罗纪蜘蛛网是一种非常有规律的蜘蛛网.如图,是由无数个正方形环绕而成的,且每一个正方形的四个顶点都恰好在它的外边最近一个正方形的四条边的三等分点上.设外围第一个正方形
的面积为
,往里第二个正方形
的面积为
,……,往里第
个正方形
的面积为
.则数列
的通项公式为______ .已知
满足
,则数列
的最大项的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5bf350a619ef25d8d9b988f3db804e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36134f01da0f13b340e82e8835324f25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a85b93ee41885756030e328542897348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/c7409d95-01a6-4043-9af4-551ba5181b75.png?resizew=150)
您最近一年使用:0次