Sn是等差数列an前n项和,若S3/S6=1/3,则S6/S12=?

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Sn是等差数列an前n项和,若S3/S6=1/3,则S6/S12=?
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Sn是等差数列an前n项和,若S3/S6=1/3,则S6/S12=?
Sn是等差数列an前n项和,若S3/S6=1/3,则S6/S12=?

Sn是等差数列an前n项和,若S3/S6=1/3,则S6/S12=?
Sn是等差数列an前n项和
则S3,S6-S3,S9-S6,S12-S9也成等差数列
因为S3/S6=1/3
故S6=3S3
所以S6-S3=2S3
所以公差是d=(S6-S3)-S3=S3
所以S9-S6=S3+2S3=3S3
S12-S9=S3+3S3=4S3
所以S9=S6+3S3=6S3
S12=S9+4S3=10S3
所以S6/S12=3S3/10S3=3/10

S3/S6=1/3得（3a1+3d）/（6a1+15d）=1/3
得a1=2d
S6/S12=（6a1+15d）/（12a1+66d）=3/10

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