已知两个等差数列{an}和{bn}的前n项和分别为An和Bn,且An/Bn=(5n+3)/(2n-1),则这两个数列的第九项之比a9/b9=,及a9/(b5+b7)+a3/(b4+b8)=.

Question

已知两个等差数列{an}和{bn}的前n项和分别为An和Bn,且An/Bn=(5n+3)/(2n-1),则这两个数列的第九项之比a9/b9=_____,及a9/(b5+b7)+a3/(b4+b8)=______.

Answer 1

A(2n-1)=[a1+a(2n-1)]*(2n-1)/2=(2n-1)an
B(2n-1)=[a1+a(2n-1)]*(2n-1)/2=(2n-1)bn
an/bn=A(2n-1)/B(2n-1)
A17=(a1+a17)*17/2=17a9
B17=(b1+b17)*17/12=17b9
a9/b9=A17/B17
=(5*17+3)/(2*17-1)
=88/33
=8/3
a9/(b5+b7)+a3/(b4+b8)
=a9/(2b6)+a3/(2b6)
=(a9+a3)/(2b6)
=2a6/(2b6)
=a6/b6
=A11/B11
=(5*11+3)/(2*11-1)
=58/21