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已知数列{an}满足a1=5,an+1=3an+2n+1(n∈N*);
(1)证明:数列{an+2n+1}是等比数列,并求出数列{an}的通项公式;
(2)若,求数列{bn}的前n项和为Sn;
(3)令,数列{cn}的前n项和为Tn,求证:.
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已知数列{an},满足a1=1,2anan+1+3an+1=3an;
(Ⅰ)求{an}的通项公式;
(Ⅱ)若,求的前2n项的和T2n.
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(本题12分)已知数列{an}中,a1=0,a2 =4,且an+2-3an+1+2an= 2n+1(),
数列{bn}满足bn=an+1-2an.
(Ⅰ)求证:数列{-}是等比数列;
(Ⅱ)求数列{}的通项公式;
(Ⅲ)求.
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已知数列{an-n}是等比数列,且满足a1=2,an+1=3an-2n+1,n∈N*.
(Ⅰ)求数列{an}的通项公式an;
(Ⅱ)求数列{an}的前n项和Sn.
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已知数列{an-n}是等比数列,且满足a1=2,an+1=3an-2n+1,n∈N*.
(Ⅰ)求数列{an}的通项公式an;
(Ⅱ)求数列{an}的前n项和Sn.
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已知数列{an} 满足an+1=3an-4n+4,n∈N*,且a1=2.若bn=an-2n+1,n∈N*,
(1)求证:{bn}为等比数列;
(2)求数列{an} 的前n项和.
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已知数列{an}满足a1=1,an+1=3an+1.
(1)证明是等比数列,并求{an}的通项公式;
(2)证明: .
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已知数列{an}满足a1=2,an+1=3an+2n-1(n∈N*).
(1)求证数列{an+n}是等比数列,并求an
(2)若数列{bn}中1>2=6,前n项和为Tn,且9Tn-a=(an+n)bn(n∈N*),求数列{bn}的通项公式.
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已知数列{an}满足a1=1,a2=3,an+2=3an+1-2an(n∈N*).
(I)证明:数列{an+1-an}是等比数列;
(II)求数列{an}的通项公式;
(III)若数列{bn}满足,证明{bn}是等差数列.
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已知数列{an}满足a1=1,a2=3,an+2=3an+1-2an(n∈N*).
(I)证明:数列{an+1-an}是等比数列;
(II)求数列{an}的通项公式;
(III)若数列{bn}满足,证明{bn}是等差数列.