在等差數(shù)列中,
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,

,則此數(shù)列前20項(xiàng)和等于( )
本題主要考查等差數(shù)列。由條件可知,

,所以

。又

,應(yīng)選B。
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知二次函數(shù)

的圖像經(jīng)過坐標(biāo)原點(diǎn),其導(dǎo)函數(shù)為

,數(shù)列

的前n項(xiàng)和為

,點(diǎn)

均在函數(shù)

的圖像上。(Ⅰ)求數(shù)列

的通項(xiàng)公式;(Ⅱ)設(shè)

,

是數(shù)列

的前n項(xiàng)和,求使得

對所有

都成立的最小正整數(shù)m.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知等差數(shù)列

的前

項(xiàng)和為

,

(1)求數(shù)列

的通項(xiàng)公式

與前

項(xiàng)和

;
(2)設(shè)

求證:數(shù)列

中任意不同的三項(xiàng)都不可能成為等比數(shù)列.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
f(x)=

x
2+

x,數(shù)列{a
n}的前n項(xiàng)和為S
n,點(diǎn)(n,S
n)(n∈N
*)均在函數(shù)y=f(x)的圖象上.
(Ⅰ)求數(shù)列{a
n}的通項(xiàng)公式a
n;
(Ⅱ)令b
n=

,求數(shù)列{b
n}的前n項(xiàng)和T
n
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科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
等差數(shù)列

的前

項(xiàng)和為

,若

,

,則該數(shù)列的公差為( )
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科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
設(shè)數(shù)列

滿足:

,那么

等于( )
A. | B.2 | C. | D.-3 |
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
(本題滿分18分,第(1)小題4分,第(2)小題6分,第(3)小題8分)
對于數(shù)列

,如果存在一個(gè)正整數(shù)

,使得對任意的

(

)都有

成立,那么就把這樣一類數(shù)列

稱作周期為

的周期數(shù)列,

的最小值稱作數(shù)列

的最小正周期,以下簡稱周期。例如當(dāng)

時(shí)

是周期為

的周期數(shù)列,當(dāng)

時(shí)

是周期為

的周期數(shù)列。
(1)設(shè)數(shù)列

滿足

(

),

(

不同時(shí)為0),且數(shù)列

是周期為

的周期數(shù)列,求常數(shù)

的值;
(2)設(shè)數(shù)列

的前

項(xiàng)和為

,且

.
①若

,試判斷數(shù)列

是否為周期數(shù)列,并說明理由;
②若

,試判斷數(shù)列

是否為周期數(shù)列,并說明理由;
(3)設(shè)數(shù)列

滿足

(

),

,

,

,數(shù)列

的前

項(xiàng)和為

,試問是否存在

,使對任意的

都有

成立,若存在,求出

的取值范圍;不存在, 說明理由;
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知{a
n}為等差數(shù)列,S
n為數(shù)列{a
n}的前n項(xiàng)和,已知S
7=7,S
15=75,
(1)求數(shù)列{a
n}的首項(xiàng)a
1及公差為d
(2)證明:數(shù)列{

}為等差數(shù)列并求其前n項(xiàng)和T
n
。
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科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
設(shè)S
n是等差數(shù)列{a
n}的前n項(xiàng)和,若

,則

等于( )
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