Question

设Sn是等差数列{An}的前n项和，若S3/S6=1/3，则S6/S12=???

Answer 1

s3=k

s6-s3=2k

s9-s6=3k

s12-s9=4k

所以

s6=3k

s9=6k

s12=10k

S6/S12=3/10
或等差数列S3,S6-S3,S9-S6,S12-S9也成等差数列
S3/S6=1/3,S6=3S3,S6-S3=2S3
S9-S6=3S3,S9=6S3
S12-S9=4S3,S12=10S3
所以S6/S12=3/10

追问

s3=k

s6-s3=2k

s9-s6=3k

s12-s9=4k

所以

s6=3k

s9=6k

s12=10k

S6/S12=3/10
依据的公式是什么啊？我不太清楚!

Answer 2

S3/S6=1/3
即 (a1 + a3)*3/[(a1 + a6)*6] = 1/3
所以 (2a1 + 2d)*3/[(2a1 + 5d)*6] = 1/3
解得 a1 = 2d
所以 S6/S12 = (a1 + a6)*6/[(a1 + a12)*12]
= (2a1 + 5d)*6/[(2a1 + 11d)*12]
= 9d*6/(15d*12)
= 3/10

Answer 3

1/9