等差数列{an}和{bn}的前n项的和分别为Sn和Tn,对一切自然数n都有SnTn=2n3n+1,则a5b5=(  ) A.23 B.914 C.2031 D.1117

问题描述:

等差数列{an}和{bn}的前n项的和分别为Sn和Tn,对一切自然数n都有

Sn
Tn
2n
3n+1
,则
a5
b5
=(  )
A.
2
3

B.
9
14

C.
20
31

D.
11
17

∵S9=

9(a1+a9)
2
=9a5,Tn=
9(b1+b9)
2
=9b5
∴a5=
1
9
S9,b5=
1
9
T9
又当n=9时,
S9
T9
=
2×9
3×9+1
=
9
14

a5
b5
=
1
9
S
9
1
9
T
9
=
S9
T9
=
9
14

故选B