設(shè)數(shù)列
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為等差數(shù)列,且a
3=5,a
5=9;數(shù)列
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的前n項(xiàng)和為S
n,且S
n+b
n="2."
(1)求數(shù)列
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,
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的通項(xiàng)公式;
(2)若
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為數(shù)列
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的前n項(xiàng)和,求
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.
試題分析:(1)由
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又有
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,當(dāng)
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時(shí) ,
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當(dāng)
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時(shí),有
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,相減得
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,即
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是等比數(shù)列,公比為
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,首項(xiàng)為1,
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.
(2)
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從而
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兩式相減得:
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點(diǎn)評:中檔題,確定數(shù)列的特征,一般要利用“定義法”或通過確定數(shù)列的通項(xiàng)公式,使問題得解。確定數(shù)列的通項(xiàng)公式,往往要建立相關(guān)元素的方程組。“裂項(xiàng)相消法”“分組求和法”“錯(cuò)位相減法”是高考�?嫉膬�(nèi)容。
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.已知
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
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
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
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,

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
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
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
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
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
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
。
(1)求

及

;
(2)令

(其中

為常數(shù),且

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
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為等差數(shù)列,

為其前

項(xiàng)和,

則
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