1 . 已知数列
满足:
,
.
(1)求
的通项公式;
(2)设
表示不超过
的最大整数,如
,
.设
,
为前
项和,求数列
的前1000项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b30e3c9bcabd41ff45d63c2aa265626e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6622931e908716637bfbb92d72e8c3ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd2f67aece6b60126de90c43047e7325.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2d8811ce6cddf86019c5c84781ad0a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6395cfb9d7bf96c2d00c3c2cdc48b81f.png)
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2024-01-09更新
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3卷引用:甘肃省武威市第八中学2023-2024学年高二上学期期末数学试题
甘肃省武威市第八中学2023-2024学年高二上学期期末数学试题(已下线)1.2.2等差数列的前n项和公式(分层练习)-2023-2024学年高二数学同步精品课堂(北师大版2019选择性必修第二册)江西省景德镇市景德镇一中2024届高三上学期1月考试数学试题
名校
解题方法
2 . 《周髀算经》记载:一年有二十四个节气,每个节气晷长损益相同(晷是按照日影测定时刻的仪器,晷长即为所测量影子的长度),夏至、小暑、大暑、立秋、处暑、白露、秋分、寒露、霜降、立冬、小雪、大雪是连续十二个节气,其日影子长依次成等差数列.经记录测算,夏至、处暑、霜降三个节气日影子长之和为16.5尺,这十二节气的所有日影子长之和为84尺,则大雪的日影子长为( )
A.1尺 | B.1.5尺 | C.11.5尺 | D.12.5尺 |
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5卷引用:甘肃省2023-2024学年高二上学期1月期末学业质量监测数学试题
甘肃省2023-2024学年高二上学期1月期末学业质量监测数学试题宁夏回族自治区银川市贺兰县第一中学2023-2024学年高二上学期期末复习数学试题(三)(已下线)1.2.2等差数列的前n项和公式(分层练习)-2023-2024学年高二数学同步精品课堂(北师大版2019选择性必修第二册)广东省广州市执信中学2024届高三上学期大湾区数学冲刺卷(一)(已下线)考点8 等差、等比数列的实际应用 2024届高考数学考点总动员【练】
解题方法
3 . 已知数列
的通项为
,前n项和为
,且
是
与2的等差中项,数列
中,
,点
在直线
上.求数列
、
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.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/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f062a8bed170de9ee318b0c69f0401b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23fc11a3a7592c68b20f93bdde2ed3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
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解题方法
4 . 已知数列
是正项数列,
是数列
的前
项和,且满足
.若
,
是数列
的前
项和,则
( )
![](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/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9583a4d9bf7b954042226232d23a8c19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea451369913dd8fd4945fe54ba1d2646.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.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/82b9eca18f6916325437d1264dbed664.png)
A.![]() | B.![]() | C.![]() | D.1 |
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2卷引用:甘肃省庆阳市华池县第一中学2023-2024学年高二上学期期中考试数学试题
5 . 已知数列
是单调递增的等比数列,数列
是等差数列,且
.
(1)求数列
与数列
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/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5171185c099ec27e5703cc00e1cf11.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec12a9a60f82467bf7bf834a9a9b1f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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295次组卷
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4卷引用:甘肃省金昌市永昌县第一高级中学2023-2024学年高二上学期期中数学试题
6 . 已知数列
的前
项和为
,且
.
(1)求数列
的通项公式;
(2)设
,数列
的前
项和为
,证明:
.
![](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/9a1db01a84a840f3cf31006bba6bcfdb.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18ec386f0f3ddad65efa9fac2d5bc5d0.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c215db1d8f69757118ad405b78035628.png)
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7 . 已知数列
的前
项和为
,若
,则( )
![](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/621bd4f533e1227c9c7f5fd6b434cb78.png)
A.4是数列![]() | B.当![]() ![]() |
C.数列![]() | D.当![]() ![]() |
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6卷引用:甘肃省金昌市永昌县第一高级中学2023-2024学年高二上学期期中数学试题
甘肃省金昌市永昌县第一高级中学2023-2024学年高二上学期期中数学试题山东省临沂市第二中学2023-2024学年高二上学期12月月考数学试题福建省三明市第一中学2023-2024学年高二上学期12月月考数学试题(已下线)4.2.3 等差数列的前n项和(8大题型)-【题型分类归纳】2023-2024学年高二数学同步讲与练(苏教版2019选择性必修第一册)青海省西宁市大通县2023-2024学年高二上学期期末考试数学试题安徽省淮南第一中学2023-2024学年高二下学期开学考试数学试题
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解题方法
8 . 已知数列
是等差数列,
,记
为数列
的前
项和,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3309d92db3265d0b74b46fa37cfa4.png)
(1)求数列
的通项公式;
(2)若
,求
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b38f54801d6b1be3e440d5d908225c04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.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/19f3309d92db3265d0b74b46fa37cfa4.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0db0cd24a55fc6ec1923631ef249995a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2023-11-27更新
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4卷引用:甘肃省酒泉市2023-2024学年高二上学期期末数学试题
9 . 已知数列是公差为1的等差数列,且
,数列
是等比数列,且
,
.
(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/c2fe6a608bad50f30a2cfda3e27db01d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b9a0d7150fb24be3e28ef7f0e18be93.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50acceaff0f9dcf1bc1e520426a68e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd85b79372dc6e596d465f738c3c300.png)
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10 . 在数列
中,若
,则数列
的前
项中所有有理项之和为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5effc331ba59f22a862f32f60ba217d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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