解题方法
1 .
的内角A,B,C的对边分别为a,b,c,已知
,
.
(1)求
面积的最大值;
(2)若
,求
的周长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acb4162c72ae8f072ce33136a21c2b47.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f82a5ec335fb8e65dcd0a12c0af06937.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2 . 已知数列
的前n项之积为
,且
,
.
(1)求
的通项公式;
(2)求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7e94265c9f21199fb1c1b0cb7dfa72d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1dbce1a21217a79f5d48a6c2733869.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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解题方法
3 . 意大利著名数学家斐波那契在研究兔子繁殖问题时,发现有这样一列数:
.该数列的特点为前两个数都是1,从第三个数起,每一个数都等于它的前面两个数的和,即
,人们把这样的一列数组成的数列
称为“斐波那契数列”,则
( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a238c89ab1b54d5fde6b18770629b91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff5e89456955d7070ab95f5b760ad9a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0232b5ad565ba5c45e2c34a130055bf.png)
A.-2024 | B.2024 | C.-1 | D.1 |
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4 . 如图,在
中,
.
,求
的长度;
(2)若
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90a4cabc24f9b7d2a9590ab1e8da4ab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de01ca42a21f0cb44b2c914e092a0d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84ebbb89ac9ec9860a8a3235c89a6182.png)
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解题方法
5 . 在①
,②
的前7项和为77,③
这三个条件中任选一个,补充在下面问题中,并解答问题.
已知等差数列
中,
,_____________.
(1)求
的通项公式;
(2)在
中每相邻两项之间插入4个数,使它们与原数列的数构成新的等差数列
,则
是不是数列
的项?若是,它是
的第几项?若不是,
,求k的值.
注:如果选择多个条件分别解答,按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0f63b0b8d22cc4fef52e36436544062.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/665aac307d4581ddcd6faf978eddbc2b.png)
已知等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)在
![](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/8a2bc7db08a8771ea47ddcb33130c937.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2261078f748f8a660ab14693f3ade978.png)
注:如果选择多个条件分别解答,按第一个解答计分.
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名校
6 . 如图,
内一点
满足
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/18/172d07aa-d865-4365-badf-c313a1b31f32.png?resizew=235)
(1)若
,求
的值;
(2)若
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/995be0729892233db17e69e11107e9c0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/18/172d07aa-d865-4365-badf-c313a1b31f32.png?resizew=235)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bcfe7e0cb0f5b2a087e40f718451936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f85f5721486bf678fa7a2be1bc079a3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1177f92b86a40a823733831470680768.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
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7 . 公差不为零的等差数列
满足
,
.
(1)求
的通项公式;
(2)记
的前
项和为
,求使
成立的最大正整数
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70a06b7117ddf935fe468034c00a3e3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25131d323ad4304473cbd09ac0c1bb02.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](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/f716bfcb3a7e9c768aa32a15da6c4679.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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8 . 数列
共有
项(常数
为大于5的正整数),对任意正整数
,有
,且当
时,
.记
的前
项和为
,则下列说法中正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a78b7628356eefcaf85df141f62369aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cf6a8bb0d46fa6cff9c985dcb6d843f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44614b27054b61277cf5c3f3d74c6736.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a78a26e3eeac053424c52ab90f6a3490.png)
![](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)
A.若![]() ![]() |
B.![]() |
C.对任意小于![]() ![]() ![]() ![]() |
D.对![]() ![]() ![]() ![]() |
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湖北省十堰市丹江口市第一中学2021-2022学年高三4月调研考试数学试题湖北省武汉市2022届高三下学期四月调研数学试题安徽省蚌埠市五河县2023届二模数学试卷(已下线)考向20等比数列及其前n项和(重点)(学生版) - 2(已下线)专题17 数列探索型、存在型问题的解法 微点3 数列探索型、存在型问题综合训练(已下线)专题05 等比数列与数列综合求和-2023-2024学年高二数学期末复习重难培优与单元检测(人教A版2019)(已下线)等差数列与等比数列
名校
解题方法
9 . 已知数列
满足
.
(1)求
的通项公式;
(2)在
和
之间插入n个数,使这
个数构成等差数列,记这个等差数列的公差为
,求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ac37a5d280f2e418b5e5a1ed66c0eb9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3468a665ac713ab7b400c672f19650a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e260b088f071983f254ce8f5163fcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0526bcbb60d5258b461ab634e913212d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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解题方法
10 . 已知函数
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f0499141930680241c2d8fc5bd1922c.png)
A.![]() ![]() ![]() | B.![]() ![]() ![]() |
C.![]() ![]() ![]() | D.![]() ![]() ![]() |
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湖北省十堰市2022届高三下学期4月调研数学试题(已下线)专题20 等差数列-2023届高考数学一轮复习精讲精练(新高考专用)广东省佛山市华南师范大学附属中学南海实验高级中学2023届高三上学期10月月考数学试题广东省广州市番禺区象贤中学2023届高三上学期10月段考数学试题1.3.1 等比数列及其通项公式(同步练习)(已下线)重难专攻(五) 数列中的综合问题 A素养养成卷(已下线)专题05 等比数列与数列综合求和-2023-2024学年高二数学期末复习重难培优与单元检测(人教A版2019)