簡介
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等差數列,如果對任意的正整數,都有(常數),則稱為等差數列,叫做公差。若三個數成等差數列,即,則稱為和的等差中項,若公差為,則,。
具體內容
在有窮等差數列中,與首末兩項距離相等的兩項和相等;並且等於首末兩項之和;特別的,若項數為奇數,還等於中間項的2倍。
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例如:在與中間插入一個數,使成等差數列,求數。
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由成等差數列,得
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即
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我們把數叫做與的等差中項。
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一般地,如果在數與中間插入一個數,使成等差數列,那么叫做與的等差中項。
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如果是,的等差中項,那么,所以
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容易看出,在等差數列中,有
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這就是說,在一個等差數列中,從第2項起,每一項(有限等差數列的末項除外)都是它的前一項與後一項的等差中項。