已知等比数列{a
n}的前n项和S
n满足:S
4-S
1=28,且a
3+2是a
2,a
4的等差中项.
(1)求数列{a
n}的通项公式;
(2)若数列{a
n}为递增数列,
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,

,问是否存在最小正整数n使得
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成立?若存在,试确定n的值,不存在说明理由.
试题分析:(1)由已知可得
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,解之得
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,
从而可得
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或
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.
(2)根据数列
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单调递增,得
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,从而

,
利用“裂项相消法”求得
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=

.
假设存在,根据
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,解得

(不合题意舍去),
依据
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为正整数,所以

的最小值为

.
(1)设等比数列

的首项为
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,公比为q,
依题意,有

,
由
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可得

得
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3分

解之得

5分
所以

或

6分
(2)因为数列

单调递增,

, 7分
所以


. 9分
假设存在,则有

,整理得:

解得

(不合题意舍去) 11分
又因为

为正整数,所以

的最小值为

. 12分
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