13-14高三上·北京朝阳·期中
名校
1 . 已知等差数列{
}的前n项和为
,且
=4,
=-5.
(1)求数列{
}的通项公式;
(2)若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45bcd8f6ede8cc2513ad41402f40086.png)
,求
的值和
的表达式.
![](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/1c58f623a748d16fab31bec339e28648.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27182444d3da4003680f07ec299087c.png)
(1)求数列{
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45bcd8f6ede8cc2513ad41402f40086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c874793d84c38eac7d575aab7a94dcd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bb192110266d1aefe5a1de2adcc927e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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2016-12-02更新
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13-14高三上·山西·阶段练习
2 . 已知数列
满足
,
,数列
满足
.
(1)证明数列
是等差数列并求数列
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/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/283b2d2e2e3a715e2a5894368d7e43c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf3613cd3c7b9fb7639a2acee7af16b.png)
(1)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求数列
![](https://img.xkw.com/dksih/QBM/2016/11/21/1573162299621376/1573162306060288/STEM/be5523c3705441f5bc01b491d0ca7108.png?resizew=32)
![](https://img.xkw.com/dksih/QBM/2016/11/21/1573162299621376/1573162306060288/STEM/3c23bfd55f3d49d8b092e0bd4b13eba8.png?resizew=19)
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3 . 在等差数列
中,已知
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ede3e77b7651bca8e3b4e83ca0b6b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6706fe00b4e231e62d9ecbec567d526b.png)
_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f322548171a35940e89f407949e1816.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ede3e77b7651bca8e3b4e83ca0b6b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6706fe00b4e231e62d9ecbec567d526b.png)
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10-11高二·福建福州·阶段练习
名校
4 . 等差数列
中,已知
=
,
,
=33,则
为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79349395e1ad2a14df8035c2d5c06cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
A.50 | B.49 | C.48 | D.47 |
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2016-12-04更新
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11-12高二·河南南阳·阶段练习
名校
5 . 设数列
的前
项和为
,已知![](https://img.xkw.com/dksih/QBM/2012/10/18/1571028585603072/1571028591263744/STEM/2f86721592834a2c8fa6e6a6408e1013.png?resizew=252)
(Ⅰ)求证:数列
为等差数列,并写出
关于
的表达式;
(Ⅱ)若数列
前
项和为
,问满足
的最小正整数
是多少?
![](https://img.xkw.com/dksih/QBM/2012/10/18/1571028585603072/1571028591263744/STEM/4a8681315d0245278303890c532e96c1.png?resizew=32)
![](https://img.xkw.com/dksih/QBM/2012/10/18/1571028585603072/1571028591263744/STEM/a076a87cc41741d5a4fbbacc07e93303.png?resizew=13)
![](https://img.xkw.com/dksih/QBM/2012/10/18/1571028585603072/1571028591263744/STEM/5b024aceef3b435c9bb4c968d6783041.png?resizew=20)
![](https://img.xkw.com/dksih/QBM/2012/10/18/1571028585603072/1571028591263744/STEM/2f86721592834a2c8fa6e6a6408e1013.png?resizew=252)
(Ⅰ)求证:数列
![](https://img.xkw.com/dksih/QBM/2012/10/18/1571028585603072/1571028591263744/STEM/c2de330e694b493b82f8c6c4fc91c0c7.png?resizew=31)
![](https://img.xkw.com/dksih/QBM/2012/10/18/1571028585603072/1571028591263744/STEM/1a00da074f784f67b663d3f963ee4a59.png?resizew=19)
![](https://img.xkw.com/dksih/QBM/2012/10/18/1571028585603072/1571028591263744/STEM/a076a87cc41741d5a4fbbacc07e93303.png?resizew=13)
(Ⅱ)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba57c83d526ac308d1461e80fcca9f36.png)
![](https://img.xkw.com/dksih/QBM/2012/10/18/1571028585603072/1571028591263744/STEM/a076a87cc41741d5a4fbbacc07e93303.png?resizew=13)
![](https://img.xkw.com/dksih/QBM/2012/10/18/1571028585603072/1571028591263744/STEM/eadc4d626d1547db83a1a45122e7e98d.png?resizew=17)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ce57e19ffb9e6db6d2ce9caa8fe977.png)
![](https://img.xkw.com/dksih/QBM/2012/10/18/1571028585603072/1571028591263744/STEM/a076a87cc41741d5a4fbbacc07e93303.png?resizew=13)
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11-12高三·山西大同·阶段练习
6 . 已知等差数列
中,
,
,
(1) 求数列
的通项公式; (2) 求数列
的前20项的和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7def23f30138e0b7c4c1e498d6903a6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1330b1d3aed077fc14ac8095cf273d20.png)
(1) 求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b91adba8efbf964e9e35547b0fd0ea36.png)
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11-12高三上·河南洛阳·期末
名校
7 . 设数列
的前
项和
满足:
,等比数列
的前
项和为
,公比为
,且
.
(1)求数列
的通项公式;
(2)设数列
的前
项和为
,求证:
.
![](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/8416d8f3b0044d515238a2cbb8164000.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/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee9dfaeae03d5f5185b513de8bbb8e54.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/ba57c83d526ac308d1461e80fcca9f36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc948ddd475d926a291c6b5eaa56da9f.png)
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11-12高三上·山西·阶段练习
8 . 已知数列
是首项
的等差数列,其前n项和为
,数列
是首项
的等比数列,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2e0f645515beb9444971af628df1b1.png)
(1)求
和
;
(2)令
,若数列
的前n项和为
,试比较
与
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.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/385275d29d8c8a7841eaeaa3dfab2cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2e0f645515beb9444971af628df1b1.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a99a7dabd56e74abc437b25970207d26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17737f07f447a21d7c8b77f4b1e8b663.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebfa6bf9e8a7fd6e7d3ed5d5600e3d62.png)
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10-11高二·山西吕梁·阶段练习
9 . 在数列
中,
=1,
,则
的值为____________
![](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/97034664bd213a31e81b9625f83d0e26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218fcd5bd1765ddb4a35c4094f16058c.png)
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10-11高二·山西吕梁·阶段练习
10 . 已知等差数列
的通项公式为
, 则它的公差是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d7022ff924c54e79baf4658148e5aca.png)
A.![]() | B.![]() | C.2 | D.5 |
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