设Sn是等差数列an的前n项和,若a5/a3=5/9,则S9/S5=

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设Sn是等差数列an的前n项和,若a5/a3=5/9,则S9/S5=
设Sn是等差数列an的前n项和,若a5/a3=5/9,则S9/S5=

设Sn是等差数列an的前n项和,若a5/a3=5/9,则S9/S5=
S9/S5
=[(a1+a9)*9/2]/[(a1+a5)*5/2]
=9/5(a1+a9)/(a1+a5)
=9/5(a1+a1+8d)/(a1+a1+4d)
=9/5(2a1+8d)/(2a1+4d)
=9/5(a1+4d)/(a1+2d)
=9/5 a5/a3
=9/5*5/9
=1