1.已知等差數(shù)列中,,則的值是( )
A.15 B.30 C.31 D.64
2.在各項(xiàng)都為正數(shù)的等比數(shù)列中,首項(xiàng),前三項(xiàng)和為21,則=( )
A.33 B.72 C.84 D.189
3.如果,,…,為各項(xiàng)都大于零的等差數(shù)列,公差,則( )
(A)(B)(C)++(D)=
4.將1,2,…,9這9個(gè)數(shù)平均分成三組,則每組的三個(gè)數(shù)都成等差數(shù)列的概率為( )
A. B. C. D.
5.已知數(shù)列( )
A. B.3 C.4 D.5
6.一給定函數(shù)的圖象在下列圖中,并且對(duì)任意,由關(guān)系式得到的數(shù)列滿足,則該函數(shù)的圖象是( )
A B C D
1.在數(shù)列{an}中,a1=1,a2=2,且則=_____.
2.設(shè)等比數(shù)列{}的公比為q,前n項(xiàng)和為,若,,成等差數(shù)列,則q的值為
1.?dāng)?shù)列的前n項(xiàng)和為S,且n=1,2,3….求
(I)的值及數(shù)列的通項(xiàng)公式;
(II)的值.
2.
已知
(Ⅰ)當(dāng)時(shí),求數(shù)列的前n項(xiàng)和
(Ⅱ)求。
3.已知是各項(xiàng)均為正數(shù)的等差數(shù)列,、、成等差數(shù)列.又,….
(Ⅰ)證明為等比數(shù)列;
(Ⅱ)如果無窮等比數(shù)列各項(xiàng)的和,求數(shù)列的首項(xiàng)和公差.
(注:無窮數(shù)列各項(xiàng)的和即當(dāng)時(shí)數(shù)列前項(xiàng)和的極限)
4.設(shè)數(shù)列的首項(xiàng),且,記
(Ⅰ)求
(Ⅱ)判斷數(shù)列是否為等比數(shù)列,并證明你的結(jié)論;
(Ⅲ)求
5.設(shè)等比數(shù)列的公比為,前n項(xiàng)和
(Ⅰ)求的取值范圍;
(Ⅱ)設(shè),記的前n項(xiàng)和為,試比較與的大小
6.已知數(shù)列
(1)證明
(2)求數(shù)列的通項(xiàng)公式an.
7.在等差數(shù)列{an}中,公差d≠0,且a2是a1和a4的等比中項(xiàng),已知a1,a3,成等比數(shù)列,求數(shù)列k1,k2,k3,…,kn的通項(xiàng)kn
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