數(shù)列{an}是首項(xiàng)a1=4的等比數(shù)列,且S3,S2,S4成等差數(shù)列. (Ⅰ)求數(shù)列{an}的通項(xiàng)公式; (Ⅱ)設(shè)bn=log2|an|,Tn為數(shù)列{1/bn?bn+1}的前n項(xiàng)和,求Tn.
數(shù)列{a
n}是首項(xiàng)a
1=4的等比數(shù)列,且S
3,S
2,S
4成等差數(shù)列.
(Ⅰ)求數(shù)列{a
n}的通項(xiàng)公式;
(Ⅱ)設(shè)b
n=log
2|a
n|,T
n為數(shù)列
{}的前n項(xiàng)和,求T
n.
優(yōu)質(zhì)解答
解 ( I)當(dāng)q=1時(shí),S
3=12,S
2=8,S
4=16,不成等差數(shù)列
當(dāng)q≠1時(shí),∵S
3,S
2,S
4成等差數(shù)列
∴2S
2=S
3+S
4∴2
=
+
得q=-2,
∴a
n=4×(-2)
n-1=(-2)
n+1( II)b
n=n+1,
∴
=
=
-
∴
Tn=(?)+
(?)+…+
(?)=
-
=
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