Question

设Sn是等差数列{An}的前项和,若A5/A3=5/9,则S9/S5等于多少?

设Sn是等差数列{An}的前项和,若A5/A3=5/9,则S9/s5等于多少?

Answer 1

因为A5/A3=5/9,不妨设A5=5,A3=9
所以S9=9(A1+A9)/2 而A1+A9=2A5 所以S9=45
而S5=5(A1+A5)/2 而A1+A5=2A3 所以S5=45
所以S9/S5=1

Answer 2

S9/s5=((a1+a9)*9/2)/((a1+a5)*5/2)
=(a1+a9)/(a1+a5)*9/5
=(2*a5/2*a3)*9/5
=1

Answer 3

A5=a+4d
A3=a+2d
(a+4d)/(a+2d)=5/9
5a+10d=9a+36d

S9=9a+9*8/2*d=9a+36d
S5=5a+5*4/2*d=5a+10d

S9/S5
=(9a+36d)/(5a+10d)
因为5a+10d=9a+36d
所以S9/S5=1