已知各項(xiàng)都不相等的等差數(shù)列{a
n}的前六項(xiàng)和為60,且a
6為a
1和a
21 的等比中項(xiàng).
(1)求數(shù)列{a
n}的通項(xiàng)公式a
n及前n項(xiàng)和S
n;
(2)若數(shù)列{b
n}滿足
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,b
1 = 3,求數(shù)列

的前n項(xiàng)和T
n.
試題分析:(1)設(shè)等差數(shù)列
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的公差為
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,由題意列方程組
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,可求得
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和
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,進(jìn)而根據(jù)等差數(shù)列的通向公式和求和公式分別求得
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和前
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項(xiàng)和
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;
(2)根據(jù)(1)中的
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和
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,根據(jù)
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,進(jìn)而求得
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,再利用裂項(xiàng)法求的
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的前項(xiàng)和.
試題解析:(1)解:設(shè)數(shù)列
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的公差是

,則
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,即
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①
∵
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為
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和

的等比中項(xiàng)
∴

,即
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②
由①②解得:
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,

∴
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,

.
(2)解:由(1)知:
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累加,得:
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
∴
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
∴
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
.
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