设Sn是等差数列an的前n项和,若S3/S6=1/3,则S6/S7=?

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设Sn是等差数列an的前n项和,若S3/S6=1/3,则S6/S7=?

设Sn是等差数列an的前n项和,若S3/S6=1/3,则S6/S7=?
设Sn是等差数列an的前n项和,若S3/S6=1/3,则S6/S7=?

设Sn是等差数列an的前n项和,若S3/S6=1/3,则S6/S7=?
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

S3=(A1+A3)x3/2,S6=[A1+A6]X6/2,S3/S6=[A1+a3]/[a1=a6]x2=1/3,
3a1+3a3=2a1+2a6,a1=2a6-3a3,a6=a1+5d,a3=a1+2d,a1=2d,s6=27d,s7=35d,
所以，s6/s7=27/35

Sn是等差数列{an}的前n项和
则S3,S6-S3,S9-S6,S12-S9也成等差数列
因为S3/S6=1/3
所以S6=3S3
故S6-S3=2S3
所以S9-S6=3S3,S12-S9=4S3
所以S9=S6+3S3=6S3
S12=S9+4S3=10S3
所以S6/S12=3S3/10S3=3/10

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