已知等差數(shù)列{a
n}的前n項和為S
n,公差d≠0,且
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成等比數(shù)列.
(1)求數(shù)列{a
n}的通項公式;
(2)設
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是首項為1,公比為3的等比數(shù)列,求數(shù)列{b
n}的前n項和T
n.
(Ⅰ)
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.(Ⅱ)
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.
試題分析:(Ⅰ)由已知
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,建立方程組
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求得
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, 從而得到通項公式
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.
此類問題突出對等差數(shù)列、等比數(shù)列基礎知識的考查,計算要細心.
(Ⅱ)不難得到
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,
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,典型的應用“錯位相消法”求和的一類問題.
在計算過程中,較易出錯的是“相減”后,和式中的項數(shù),應特別注意.
試題解析:(Ⅰ)依題意得
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解得
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,
∴
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,
即
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.
(Ⅱ)
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,
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兩式相減得,
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=
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.
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