设Sn是等差数列an的前n项和,若S5/S3=5/9,则S9/S5=

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设Sn是等差数列an的前n项和,若S5/S3=5/9,则S9/S5=
设Sn是等差数列an的前n项和,若S5/S3=5/9,则S9/S5=

设Sn是等差数列an的前n项和,若S5/S3=5/9,则S9/S5=
s5/s3=5(a1+a5)/3(a1+a3)=5a3/3a2=5/9
因此a2=3a3
故公差是a3-a2=-2a3
故a4=a3-2a3=-a3
a5=a4-2a3=-3a3
s9/s5=9(a1+a9)/5(a1+a5)=9a5/5a3=(9/5)*(-3)=-27/5

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