已知两个等差数列{an}和{bn}的前n和分别为An和Bn,且AnBn=2n+1n+3,则a9b9=______.-数学

题目简介

已知两个等差数列{an}和{bn}的前n和分别为An和Bn,且AnBn=2n+1n+3,则a9b9=______.-数学

题目详情

已知两个等差数列{an}和{bn}的前n和分别为An和Bn,且
An
Bn
=
2n+1
n+3
,则
a9
b9
=______.
题型:填空题难度:中档来源:不详

答案

∵两个等差数列{an}和{bn}的前n和分别为An和Bn,
An
Bn
=class="stub"2n+1
n+3

a9
b9
=
2a9
2b9
=
a1+a17
b1+b17

=
class="stub"17
2
(a1+a17)
class="stub"17
2
(b1+b17)
=
A17
B17

=class="stub"2×17+1
17+3
=class="stub"7
4

故答案为:class="stub"7
4

更多内容推荐