等差数列an,bn的前n项和的比为Sn:Sn''=5n+3:2n+7,则a5:b5=?

问题描述:

等差数列an,bn的前n项和的比为Sn:Sn''=5n+3:2n+7,则a5:b5=?

a5:b5
=9a5:9b5
=s9:s"9
=(5*9+3):(2*9+7)
=48:25

因为2a5=a1+a9=a2+a8=a3+a7=a4+a6
所以a5:b5=9a5:9b5=a1+...+a9:b1+...b9=S9:S9"=45+3:18+7=48:25

因为等差数列的前9项的均值等于第五项
a5:b5=S9:S9''
n=9带入Sn:Sn''=5n+3:2n+7,
得a5:b5=48:25