已知等差數(shù)列

的前n項和為

,且

,

.
(1)求數(shù)列

的通項

;(2)設(shè)

,求數(shù)列

的前n項和

.
(Ⅰ)

;(Ⅱ)

.
試題分析:(Ⅰ)由等差數(shù)列的通項公式

和等差數(shù)列的前

項和公式

可求首項

和公差

,從而求等差數(shù)列的通項

.
(Ⅱ)利用數(shù)列分組求和的方法,分別求等比數(shù)列和等差數(shù)列的和,即可得數(shù)列

的前n項和

.
試題解析:(Ⅰ)設(shè)等差數(shù)列

的首項為

,公差為

.因為

,

,
所以有

,故

.
(Ⅱ)由(Ⅰ)有

,所以

.

考點:

;2、等差數(shù)列的前

項和公式

;3、等比數(shù)列的前

項和為

;4、數(shù)列分組求和.
練習(xí)冊系列答案
相關(guān)習(xí)題
科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知等差數(shù)列

中,

.
(I)求數(shù)列

的通項公式;
(II)若數(shù)列

的前

項和

,求

的值.
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知數(shù)列{an}滿足:a1=20,a2=7,an+2﹣an=﹣2(n∈N*).
(Ⅰ)求a3,a4,并求數(shù)列{an}通項公式;
(Ⅱ)記數(shù)列{an}前2n項和為S2n,當(dāng)S2n取最大值時,求n的值.
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
設(shè)不等式組

所表示的平面區(qū)域為D
n,記D
n內(nèi) 的整點個數(shù)為a
n(n∈N
*)(整點即橫坐標(biāo)和縱坐標(biāo)均為整數(shù)的點).
(1) 求證:數(shù)列{a
n}的通項公式是a
n=3n(n∈N
*).
(2) 記數(shù)列{a
n}的前n項和為S
n,且T
n=

.若對于一切的正整數(shù)n,總有T
n≤m,求實數(shù)m的取值范圍.
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知數(shù)列

滿足:

數(shù)列

滿足

。
(1)若

是等差數(shù)列,且

求

的值及

的通項公式;
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
設(shè)數(shù)列

,

,若以

為系數(shù)的二次方程:

都有根

滿足

.
(1)求證:

為等比數(shù)列
(2)求

.
(3)求

的前

項和

.
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
等差數(shù)列

的公差不為零,首項

,

是

和

的等比中項,則數(shù)列的前

項之和是 ( )
查看答案和解析>>