问题 选择题
等差数列{an}{bn}前n项和分别为Sn,Tn,
Sn
Tn
=
3n+15
n+2
,则使
an
bn
为整数的正整数n有(  )
A.1个B.2个C.3个D.大于3个
答案

an
bn
=
2an
2bn
=
a1+a2n-1
b1+b2n-1
=
(2n-1)(a1+a2n-1)
2
(2n-1)(b1+b2n-1)
2
=
S2n-1
T2n-1

因为

Sn
Tn
=
3n+15
n+2

所以

an
bn
=
3(2n-1)+15
2n-1+2
=
6n+12
2n+1
=3+
9
n+1

当n=2,8时,

an
bn
为整数,

故选B.

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