1 . 在各项均为正数的等差数列
中,
,
,
成等比数列,
.
(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/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/614206299653e4111ac285f5375e34c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc17ca3ab612ea9cf6cfa1eea53cb1eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b50b3927041221a53f19b6a0549d71.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设数列
![](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/8d3440b0ed9f4b71cf7a52f557f97160.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6de09cc78d67d04048a61fc5bbca1e2c.png)
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2023-04-14更新
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1142次组卷
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2卷引用:安徽省泗县第一中学2022-2023学年高二下学期第二次月考数学试卷
2 . 已知
满足
,若
表示大于
的最小整数,如
,设
,则数列
的前2022项和为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fb4f083f0a347f64335e2e2d8b8e5a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1efe124c3e4a990276cfd12d6e6ecce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26a905138be720495250241021c7c87d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe89a0df965c81aa42c0f1f8009cfc66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
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解题方法
3 . 已知两个等差数列
和
的前n项和分别为
和
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa1f959646f47d0b32bfa6a3411ae55f.png)
_____________ .
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c4dc12207b2b6bfb6cdf14fdd883ba4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa1f959646f47d0b32bfa6a3411ae55f.png)
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4 . 已知数列
满足
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8297328cdd3932e1ed4bdb4b5612276e.png)
A.![]() | B.![]() |
C.![]() ![]() | D.![]() |
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5 . 已知
是等差数列
的前n项和,且
,
,则下列选项正确的是( )
![](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/ff1508953a6b81848a89411596db8c00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/345eaa86e163b97a37552f636b587e73.png)
A.数列![]() | B.![]() | C.![]() ![]() | D.![]() |
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6 . 求值:
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33edf4221e3672cd71dc89e85dd1693.png)
A.1013 | B.-1012 | C.-1013 | D.1012 |
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7 . 在等差数列
中,若
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218fc022977dbf9c5b5c3c6b6dcf201e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a889e13ba8518fa34494ed1295078999.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af1f1b7e9e20d799ee3c06b89a0611c.png)
A.40 | B.50 | C.60 | D.70 |
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8 . 已知等差数列
的前n项和为
,其中
,
;等比数列
的前n项和为
,其中
,
.
(1)求数列
,
的通项公式;
(2)记
,求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30bdfae11981d18addc88f51770ecc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9503e00ed41350e911c6f287da15ca9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/725fced78a6d16c487461fb1cdf95409.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ac60c4774bfd240de1629b1490e22f.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed90e38d84b4cda2c031333396679172.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15520cf5be7c2685975aac51bc99ac4f.png)
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2022-11-13更新
|
916次组卷
|
5卷引用:安徽省宿州市砀山中学2022-2023学年高三上学期11月段考数学试题
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解题方法
9 . 已知数列
的前n项和为
,且
成等差数列,若
,则使得
,
同时成立的k的值为_________________ .
![](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/97c14d9ae06f864498048d55088ff4e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28dd4503d6b016c84426f2e74555b4e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65f932e3cd854fa8bcb0197e0dbca591.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2998fe913308b7d045f78f4e50938a.png)
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2022-11-13更新
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423次组卷
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5卷引用:安徽省宿州市砀山中学2022-2023学年高三上学期11月段考数学试题
安徽省宿州市砀山中学2022-2023学年高三上学期11月段考数学试题江西省抚州市金溪县第一中学2023届高三上学期11月段考数学(理)试题(已下线)4.2 等差数列(5)(已下线)模块二 数列 不等式-2(新)1号卷·A10联盟2023届高三上学期11月段考数学试卷
10 . 已知数列{an}为各项非零的等差数列,其前n项和为Sn,满足
.
(1)求数列{an}的通项公式;
(2)记
,求数列{bn}的前n项和Tn.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92094e8e4784c241c72089b93565abc5.png)
(1)求数列{an}的通项公式;
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8869767a953b3f85abb4685d7cce858.png)
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2022-01-09更新
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5卷引用:安徽省宿州市萧县鹏程中学2021-2022学年高二下学期第一次质量检测数学试题
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