设Sn是等差数列｛an｝的前n项之和,若S3/S6=1/3,则S6/S16=（）.（请详细说明.）A.27/152B.1/3C.1/8D.25/152

Question

设Sn是等差数列｛an｝的前n项之和,若S3/S6=1/3,则S6/S16=（ ）.
（请详细说明.）A.27/152 B.1/3
C.1/8 D.25/152

Answer 1

S16 = 16a1 + 120*p
S6 = 6a1 + 15*p
S3 = 3a1 + 3*p
S3/S6 = (a1+p)/(2a1+5p) = 1/3
=> a1=2p
S6/S16 = (12+15)/(32+120)
= 27/152
选A
（其中a1为首项,p为公差）