设两个等差数列{an}和{bn}的前n项和分别是Sn和Tn,且Sn/Tn=n+3/3n+2(n∈N*),则a7/b7的值是___
问题描述:
设两个等差数列{an}和{bn}的前n项和分别是Sn和Tn,且Sn/Tn=n+3/3n+2(n∈N*),则a7/b7的值是___
答
等差
a1+a13=2a7
b1+b13=2b7
所以
a7/b7
=2a7/2b7
=[(a1+a13)*13/2]/[(b1+b13)*13/2]
=S13/T13
=(13+3)/(39+2)
=16/41