已知数列{an}是等差数列,a1=2,a1+a2+a3=12,(1)求数列{an}的通项公式; (2)令bn=3an求数列{bn}的前

2025-05-12 22:52:32
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回答1:

(1)∵数列{an}为等差数列
由a1+a2+a3=12可得3a2=12
∴a2=4,又a1=2∴d=2,
数列的通项公式为an=2n
(2)由(1)可得bn=32n=9n
{bn}是首项为9,公比为9的等比数列
Sn

9(1?9n)
1?9
9
8
(9n?1)
(3)由(1)知 Cn
1
2n(2n+2)
1
4n(n+1)
=
1
4
(
1
n
?
1
n+1
)

Tn=C1+C2+…+Cn
=
1
4
(1?
1
2
+
1
2
?
1
3
+…+
1
n
?
1
n+1
)

=
1
4
(1?
1
n+1
)
=
n
4(n+1)