已知两等差数列{an},{bn}的前n项和分别为Sn,Tn,且SnTn=2n+1n+2,则a8b7=______.-数学

题目简介

已知两等差数列{an},{bn}的前n项和分别为Sn,Tn,且SnTn=2n+1n+2,则a8b7=______.-数学

题目详情

已知两等差数列{an},{bn}的前n项和分别为Sn,Tn,且
Sn
Tn
=
2n+1
n+2
,则
a8
b7
=______.
题型:填空题难度:中档来源:不详

答案

设Sn=kn(2n+1),Tn=kn(n+2),(k≠0),
∵数列{an},{bn}是等差数列,
∴an=3k+4k(n-1)=4kn-k,bn=3k+2k(n-1)=2kn+k,
a8
b7
=class="stub"32k-k
14k+k
=class="stub"31
15

故答案为class="stub"31
15

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