已知等差数列{an} S3:S6=1/3S6:S12=?_数学解答

已知等差数列{an}
S3:S6=1/3
S6:S12=?

人气：345 ℃　时间：2020-05-14 03:08:52

解答

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