两个等差数列{an}和{bn}的前n项和分别是Sn和Tn,Sn/Tn=2n+3/3n-1,求a9/b9

问题描述:

两个等差数列{an}和{bn}的前n项和分别是Sn和Tn,Sn/Tn=2n+3/3n-1,求a9/b9

{an}和{bn}公差分别设为d1、d2
Sn=na1+n(n-1)d1/2
Tn=nb1+n(n-1)d2/2
Sn/Tn=[2a1+(n-1)d1]/[2b1+(n-1)d2]=(2n+3)/(3n-1) (1)
令n=17代入(1)式:
(2a1+16d1)/(2a2+16d2)=(a1+8d1)/(b1+8d2)=a9/b9=37/50
a9/b9=37/50