已知等差数列{an} S3:S6=1/3S6:S12=?
问题描述：
已知等差数列{an}
S3:S6=1/3
S6:S12=?
答
S3:S6=1/3
[(2a1+2d)*3/2]/[(2a1+5d)*6/2]=1/3
a1=2d
S6:S12=[(2a1+5d)*6/2]/[(2a1+11d)*12/2]=3/10
答
S3=A1+A2+A3=3A1+3D S6=6A1+15D 因为S3/S6=1/3 所以A1=2D 所以S6/S12=3/10
答
S3/S6=[(a1+a3)*3/2]/[(a1+a6)*6/2]=1/3
(9/2)(a1+a3)=3(a1+a6)
3(a1+a1+2d)=2(a1+a1+5d)
6a1+6d=4a1+10d
a1=2d
S6/S12=[(a1+a6)*6/2]/[(a1+a12)*12/2]
=(1/2)(a1+a1+5d)/(a1+a1+11d)
=(1/2)(4d+5d)/(4d+11d)
=3/5
答
S3,S6-S3,S9-S6,S12-S9成等差数列.设要s3 为m ,s6为3m.
m, 2m, 3m , 4m, 所以S12是10m,
s6:s10=3:10