Question

设Sn是等差数列的前n项和.若S3/S7=1/3,则S6/S7=?答案是27/35

Answer 1

S3/S6=1/3

S6=3S3

6a1+15d=3(3a1+3d)

-3a1=-6d

a1=2d

所以 an=2d+(n-1)d=(n+1)d

Sn=n(2+n+1)d/2=n(3+n)d/2

S6/S7=(6×9)/(7×10)=27/35