设等差数列{an}的前n和为Sn,若a7/a4=3,则S5/a5的值为

Question

设等差数列{an}的前n和为Sn,若a7/a4=3,则S5/a5的值为

Answer 1

a7=3a4
a1+6d=3(a1+3d)=3a1+9d
a1=-3d/2
a5=a1+4d=5d/2
所以a1/a5=-3/5
S5=(a1+a5)*5/2
S5/a5=5/2*(a1+a5)/a5=5/2*(a1/a5+1)=5/2*(-3/5+1)=1