设等差数列{an}的前n项和为Sn,且a5=3a7,则S9/S13=?

问题描述:

设等差数列{an}的前n项和为Sn,且a5=3a7,则S9/S13=?

a1+a9=a1+a1+8d=2a1+8d=2(a1+4d)=2a5
a1+a13=a1+a1+12d=2a1+12d=2(a1+6d)=2a7
s9=(a1+a9)*9/2=9a5
S13=13a7
S9/S13=9a5/13a7=9×3a7/13a7=27/13