问题 填空题
等差数列{an}和{bn}的前n项和分别为Sn和Tn,且
Sn
Tn
=
2n
3n+1
,则
a5
b5
=______.
答案

Sn
Tn
=
2n
3n+1
=
n(a1+an
2
n(b1+bn
2
=
a1+an
b1+bn

a5
b5
=
9
2
(a1+a9
9
2
(b1+b9
=
a1+a9
b1+b9

即当n=9时,

a5
b5
=
Sn
Tn
=
2n
3n+1
=
18
28
=
9
14

故答案为

9
14

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