本題考查等差數(shù)列的性質(zhì)和前n項和公式.
等差數(shù)列
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中,若
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則
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于是
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所以
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科目:高中數(shù)學
來源:不詳
題型:解答題
已知無窮數(shù)列
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中,
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是首項為
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,公差為
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的等差數(shù)列;
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是首項為
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,公比為
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的等比數(shù)列
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,并對任意
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,均有
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成立,(1)當
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時,求
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; (2)若
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,試求
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的值;(3)判斷是否存在
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,使
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成立,若存在,求出
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的值;若不存在,請說明理由.
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科目:高中數(shù)學
來源:不詳
題型:單選題
設(shè)等差數(shù)列
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的前
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項和為
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,若
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,
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,則
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,
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,
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,
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中最大的是( )
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科目:高中數(shù)學
來源:不詳
題型:解答題
已知等差數(shù)列{
an}的前
n項的和記為
Sn.如果
a4=-12,
a8=-4.
(1)求數(shù)列{
an}的通項公式;
(2)求
Sn的最小值及其相應(yīng)的
n的值;
(3)從數(shù)列{
an}中依次取出
a1,
a2,
a4,
a8,…,
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,…,構(gòu)成一個新的數(shù)列{
bn},求{
bn}的前
n項和.
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科目:高中數(shù)學
來源:不詳
題型:解答題
已知數(shù)列
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的相鄰兩項
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、
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是關(guān)于
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的方程
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的兩根,且
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。
(1)求證:數(shù)列
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是等比數(shù)列;
(2)求數(shù)列
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的前
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項的
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和及數(shù)列
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的通項公式。
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科目:高中數(shù)學
來源:不詳
題型:解答題
已知數(shù)列
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的前
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項和為
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,數(shù)列
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滿足:
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,前
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項和為
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,設(shè)
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。 (1)求數(shù)列
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的通項公式;
(2)是否存在自然數(shù)k, 當
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時,總有
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成立,若存在,求自然數(shù)
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的最小值。若不存在,說明理由。
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科目:高中數(shù)學
來源:不詳
題型:解答題
(本題12分)等比數(shù)列
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中,已知
(I)求數(shù)列
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的通項公式;
(Ⅱ)若
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分別為等差數(shù)列
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的第3項和第5項,試求數(shù)列
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的通項公式及前
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項和
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。
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科目:高中數(shù)學
來源:不詳
題型:單選題
定義:在數(shù)列{a
n}中,若滿足-=d(n∈N
*,d為常數(shù)),我們稱{a
n}為“比等差數(shù)列”.已知在“比等差數(shù)列”{a
n}中,a
1=a
2=1,a
3=2,則的個位數(shù)字是( )
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科目:高中數(shù)學
來源:不詳
題型:解答題
已知數(shù)列
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的各項均為正數(shù),
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是數(shù)列
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的前
n項和,且
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.
(1)求數(shù)列
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的通項公式;
(2)
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的值.
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