傳說古希臘畢達(dá)哥拉斯學(xué)派的數(shù)學(xué)家經(jīng)常在沙灘上面畫點或用小石子表示數(shù).他們研究過1,3,6,10,…,可以用如圖的三角形點陣表示,那么第10個點陣表示的數(shù)是
.
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試題分析:
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,
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,
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,
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,
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,
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,解題的關(guān)鍵是由題設(shè)得出相鄰兩個三角形數(shù)的遞推關(guān)系,由此列舉出三角形數(shù),本題綜合性強,有一定的探究性,是高考的重點題型,解答時要注意總結(jié)其中的規(guī)律.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知數(shù)列
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的首項
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其中
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,
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令集合
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.
(Ⅰ)若
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,寫出集合
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中的所有的元素;
(Ⅱ)若
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,且數(shù)列

中恰好存在連續(xù)的7項構(gòu)成等比數(shù)列,求
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的所有可能取值構(gòu)成的集合;
(Ⅲ)求證:
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.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知
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是正數(shù)列組成的數(shù)列,
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,且點
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在函數(shù)

的圖像上,
(Ⅰ)求
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的通項公式;
(Ⅱ)若數(shù)列
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滿足
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,
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,求證:
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.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知數(shù)列

的前
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項和為
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,若
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,
⑴證明數(shù)列
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為等差數(shù)列,并求其通項公式;
⑵令
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,①當(dāng)
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為何正整數(shù)值時,
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:②若對一切正整數(shù)
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,總有
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,求
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的取值范圍.
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科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
已知各項為正數(shù)的等差數(shù)列
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的前
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項和為
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,那么
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的最大值為( )
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科目:高中數(shù)學(xué)
來源:不詳
題型:填空題
下列命題中,真命題的序號是
.
①
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中,
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②數(shù)列{
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}的前n項和
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,則數(shù)列{
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}是等差數(shù)列.
③銳角三角形的三邊長分別為3,4,
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,則
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的取值范圍是
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.
④等差數(shù)列{
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}前n項和為
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。已知
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+

-

=0,
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=38,則m=10.
⑤常數(shù)數(shù)列既是等差數(shù)列又是等比數(shù)列.
⑥數(shù)列{

}滿足,

,則數(shù)列{

}為等比數(shù)列.
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科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
設(shè)等差數(shù)列{
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}的前n項和為
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,已知

=-2012,

=2,則
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=( )
A.-2013 | B.2013 | C.-2012 | D.2012 |
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科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
設(shè)
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是公差為正數(shù)的等差數(shù)列,

則

( )
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科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
設(shè)

是等差數(shù)列
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的前
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項和,
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,則
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( )
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