Question

在等差数列an中，已知a3:a5=3:4,S9:S5=?

请写出详细过程

Answer 1

因a3:a5=3:4,即(a1+2d):(a1+4d)=3:4,d为公差，解得a1=4d.
s9=（a1+a9)*9/2=[4d+(4d+8d)]*9/2=72d
s5=(a1+a5)*5/2=[4d+(4d+4d)]*5/2=30d
s9:s5=72d:30d=12:5

Answer 2

an=a1+(n-1)d
a3/a5 = (a1+2d)/(a1+4d)=3/4
S9/S5= [9(2a1+8d)/2]/[5(2a1+4d)/2]
= (9/5)(a1+4d)/(a1+2d)
=(9/5)(4/3)
=12/5

Answer 3

4(a1+2d)=3(a1+4d)
a1=4d
S9=(a1+a9)*9/2=(4d+4d+8d)*9/2
S5=(a1+a5)*5/2=(4d+4d+4d)*5/2
S9:S5=16*9/12*5=36:15

Answer 4

十二比五