數(shù)列

中,

,

,

.
(Ⅰ)證明:數(shù)列

是等比數(shù)列,并求

;
(Ⅱ)求數(shù)列

的前

項(xiàng)和

.
(Ⅰ)

又

,知

是以3為首項(xiàng)、3為公比的等比數(shù)列

,即


.
(Ⅱ)由(Ⅰ)知
故

.
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
對于數(shù)列

,定義

為數(shù)列

的一階差分?jǐn)?shù)列,其中

;對

,定義

為

的

階差分?jǐn)?shù)列,其中

.
(1)若數(shù)列

的通項(xiàng)公式為

,分別求出其一階差分?jǐn)?shù)列

、二階差分?jǐn)?shù)列

的通項(xiàng)公式;
(2)若數(shù)列

首項(xiàng)

,且滿足

,求出數(shù)列

的通項(xiàng)公式

及前

項(xiàng)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
“

”是“a,b,c成等比數(shù)列”的( )
A.充分不必要條件. | B.必要不充分條件. |
C.充要條件. | D.既不充分也不必要條件. |
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
等比數(shù)列

的各項(xiàng)均為正數(shù),且

,則

().
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
在數(shù)1和100之間插入

個(gè)實(shí)數(shù),使得這

個(gè)數(shù)構(gòu)成遞增的等比數(shù)列,將這

個(gè)數(shù)的乘積記作

,再令


.
(Ⅰ)求數(shù)列

的通項(xiàng)公式;
(Ⅱ)設(shè)

求數(shù)列

的前

項(xiàng)和

.
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已數(shù)列

滿足
a1 = 1,
a2 = 3,

,

.
(1) 證明:數(shù)列

為等比數(shù)列;
(2) 求數(shù)列

的通項(xiàng)公式;
(3)

,

的前
n項(xiàng)和為

,求證

.
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知等比數(shù)列

分別是某等差數(shù)列的第5項(xiàng)、第3項(xiàng)、第2項(xiàng),且

(Ⅰ)求

;
(Ⅱ)設(shè)

,求數(shù)列

的前

項(xiàng)和

查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:填空題
在等比數(shù)列{an}中,a1+a2=3,a2+a3=6,則此數(shù)列的前10項(xiàng)之和為 .
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
已知

是等比數(shù)列,

=4,

=32,則

=( )
查看答案和解析>>