等差数列{an},{bn}前n项和分别为An,Bn,若AnBn=n2n+1(n∈N+)且B2=20,则an=______.-数学

题目简介

等差数列{an},{bn}前n项和分别为An,Bn,若AnBn=n2n+1(n∈N+)且B2=20,则an=______.-数学

题目详情

等差数列{an},{bn}前n项和分别为An,Bn,若
An
Bn
=
n
2n+1
 (n∈N+)且B2=20,则an=______.
题型:填空题难度:偏易来源:不详

答案

An
Bn
=class="stub"n
2n+1
,∴
a1
b1
=class="stub"1
3
,∴b1=3a1,
a1a2
20
=class="stub"2
5
,∴a1+a2=8  ①,
a1+a3
b1+b3
=class="stub"3
7
,a1+a3=class="stub"3
7
 (b1+b3 )=class="stub"3
7
•2b2=class="stub"6
7
 ( 20-3a1 ),
∴25a1+7a3=120  ②,由①②可得  a1=2,公差d=4,∴an =4n-2,
故答案为:4n-2.

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