有两个等差数列{an}{bn},若(a1+a2+.+an)/(b1+b2+.+bn)=(3n-1)/(2n+3)则a13
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有两个等差数列{an}{bn},若(a1+a2+.+an)/(b1+b2+.+bn)=(3n-1)/(2n+3)则a13/b13=?
设数列{an}前n项和为Sn,公差为d;数列{bn}前n项和为Tn,公差为d'.
Sn/Tn=[na1+n(n-1)d/2]/[nb1+n(n-1)d'/2]
=[2a1+(n-1)d]/[2b1+(n-1)d']
=[(2a1-d)+nd]/[(2b1-d')+nd']
=(a1+a2+...+an)/(b1+b2+...+bn)
=(3n-1)/(2n+3)
令d=3t,则2a1-d=-t,d'=2t,2b1-d'=3t.
解得
a1=t,d=3t,b1=2.5t,d'=2t
a13/b13=(a1+12d)/(b1+12d')
=(t+12×3t)/(2.5t+12×2t)
=74/53
Sn/Tn=[na1+n(n-1)d/2]/[nb1+n(n-1)d'/2]
=[2a1+(n-1)d]/[2b1+(n-1)d']
=[(2a1-d)+nd]/[(2b1-d')+nd']
=(a1+a2+...+an)/(b1+b2+...+bn)
=(3n-1)/(2n+3)
令d=3t,则2a1-d=-t,d'=2t,2b1-d'=3t.
解得
a1=t,d=3t,b1=2.5t,d'=2t
a13/b13=(a1+12d)/(b1+12d')
=(t+12×3t)/(2.5t+12×2t)
=74/53
有两个等差数列an,bn,若Sn/Tn=a1+a2+.an/b1+b2+---+bn=3n-1/2n+3,则a13/b1
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