设Sn是等差数列An的前n项和,若S3/S6=1/3,则S6/S12等于

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设Sn是等差数列An的前n项和,若S3/S6=1/3,则S6/S12等于

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

设Sn是等差数列An的前n项和,若S3/S6=1/3,则S6/S12等于
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

Sn是等差数列
所以S3,S6-S3,S9-S6,S12-S9是等差数列
设S3=A.S6=3A,则S6-S3=2A,S9-S6=3A,S12-S9=4A
S9=6A,S12=10A
则S6/S12等于3/10

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