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1 . 已知数列
的前
项和
,则( )
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](/uploads/image/squformula/57f80f832e1b7f5195c06a23de08083b.png)
a.![]() | b.![]() |
c.数列![]() ![]() ![]() | d.![]() |
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2 . 已知数列
的前
项和为
.
(1)若
,求和:;
(2)若
,证明:
是等差数列.
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](/uploads/image/squformula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)若
![](/uploads/image/squformula/0ff1c33b81ac2f065d37faef37504bb9.png)
(2)若
![](/uploads/image/squformula/a833791dde24743185721660a8ebfb65.png)
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
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3 . 已知数列
满足
,
,
数列
,
的前n项和分别为.
(1)求
,并证明数列
为等比数列;
(2)当
时,有恒成立,求正整数m的最小值.
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/b13a6e1d671215fc96e4bee3541d1096.png)
![](/uploads/image/squformula/60d3eaf50c4cacfbe369e12984e8b31a.png)
![](/uploads/image/squformula/a784243ca60ed9fa55480c6987d40605.png)
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/034ba25825c13725931c483aa47c9363.png)
(1)求
![](/uploads/image/squformula/d7de777f1b9ad8ffaf3568c093b2f7c5.png)
![](/uploads/image/squformula/c8194a62bc60a9da9b5cf76f9dc0fa09.png)
(2)当
![](/uploads/image/squformula/856b137a34d2d5b20671b7a3c7a29606.png)
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4 . 已知等差数列
的前
项和为
,若
,公差
,则
的最小值为( )
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](/uploads/image/squformula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](/uploads/image/squformula/4ac577f987d768e1a115f2747ec0fd6d.png)
![](/uploads/image/squformula/c5c1344592c925b273f2cb9b9e47ebbb.png)
![](/uploads/image/squformula/08eb71ecf8d733b6932f4680874dbbf3.png)
a.![]() | b.![]() | c.![]() | d.![]() |
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5 . 在等差数列
中,
.
(1)求
的通项公式;
(2)若
,求数列
的前
项和
.
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/0c829f05f89e6ed594393c20e5964a4f.png)
(1)求
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](/uploads/image/squformula/986babee20ac8ba50add7fe442e08173.png)
![](/uploads/image/squformula/034ba25825c13725931c483aa47c9363.png)
![](/uploads/image/squformula/e2d51f9147b8265c0276c1f2c2659197.png)
![](/uploads/image/squformula/3b9a0d7150fb24be3e28ef7f0e18be93.png)
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解题方法
6 . 已知
为数列
的前
项和,满足
,数列
是等差数列,且
.
(1)求数列
和
的通项公式;
(2)求数列
的前
项和.
![](/uploads/image/squformula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](/uploads/image/squformula/f985ba3b26e98eff61d15c39e627fa21.png)
![](/uploads/image/squformula/034ba25825c13725931c483aa47c9363.png)
![](/uploads/image/squformula/74cddbec05eb7aecc2f229f5fdf9c8dd.png)
(1)求数列
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/034ba25825c13725931c483aa47c9363.png)
(2)求数列
![](/uploads/image/squformula/5344eadd4711db34e3f935aedd5fb270.png)
![](/uploads/image/squformula/b6a24198bd04c29321ae5dc5a28fe421.png)
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7 . 已知数列
的通项公式为
,数列
的通项公式为
,
为正整数,若数列
中去掉
的项后,余下的项按原顺序组成数列
,则![](/uploads/image/squformula/58df886060a866eeeddb6b666a0e680b.png)
______ .
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/e21a2abecb477ad5ff15db0f3d7817f3.png)
![](/uploads/image/squformula/034ba25825c13725931c483aa47c9363.png)
![](/uploads/image/squformula/15ff259bff098430a6512d0e4f6fb2d9.png)
![](/uploads/image/squformula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](/uploads/image/squformula/034ba25825c13725931c483aa47c9363.png)
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/57ef6d44448092ebdb9e4a49d866a749.png)
![](/uploads/image/squformula/58df886060a866eeeddb6b666a0e680b.png)
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8 . 已知a,b,c三点在直线l上,点o在直线l外,满足
,其中,
为等差数列
中的项,记
为数列
的前n项和,则
( )
![](/uploads/image/squformula/ff7848136f3f20981b6d616f9c195a6f.png)
![](/uploads/image/squformula/f11075f2c574b6c59b97fb3038000e38.png)
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/780019495df34d40fff9d8f31bbf3e74.png)
a.1010 | b.1011 | c.1012 | d.1013 |
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9 . 已知数列
是各项为正数的数列,前n项和记为
,
,(
),
(1)求数列
的通项公式;
(2)设
,
,求数列
的前n项和
.
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](/uploads/image/squformula/16789712fe64778f607d9d84a9094b54.png)
![](/uploads/image/squformula/e97769855336d73371930df1f187875e.png)
(1)求数列
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](/uploads/image/squformula/adefc7f406cfc667c0f8f51348d5febc.png)
![](/uploads/image/squformula/e97769855336d73371930df1f187875e.png)
![](/uploads/image/squformula/034ba25825c13725931c483aa47c9363.png)
![](/uploads/image/squformula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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解题方法
10 . 设等差数列
的前
项和为
,若
,
,则
( )
![](/uploads/image/squformula/4f5011f62c285c73e9baddd16f485777.png)
![](/uploads/image/squformula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](/uploads/image/squformula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](/uploads/image/squformula/8ad088f3ec8297e74e50a01e5e76b0cc.png)
![](/uploads/image/squformula/e2a55aadc0a7cd1b97eced4e34793f5e.png)
![](/uploads/image/squformula/5af1f1b7e9e20d799ee3c06b89a0611c.png)
a.![]() | b.![]() | c.![]() | d.![]() |
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