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)

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

等差数列,前n项和An,Bn都含n这个因式
设An/Bn约单项式 nk
则An=(5n+3)nk，Bn=(2n-1)nk
an=An-A(n-1)=(10n-2)k
bn=Bn-B(n-1)=(4n-3)k
a9=88k，b9=33k
a9/b9=88/33=8/3
a9/(b5+b7)+a3/(b4+b8)

=88k/(17k+25k)+28k/(13k+29k)
=88k/42k+28k/42k
=116k/42k
=58/21

Answer 2

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