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=?
![有两个等差数列{an}{bn},若(a1+a2+.+an)/(b1+b2+.+bn)=(3n-1)/(2n+3)则a13](/uploads/image/z/1605255-15-5.jpg?t=%E6%9C%89%E4%B8%A4%E4%B8%AA%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%7Ban%7D%7Bbn%7D%2C%E8%8B%A5%28a1%2Ba2%2B.%2Ban%29%2F%28b1%2Bb2%2B.%2Bbn%29%3D%283n-1%29%2F%282n%2B3%29%E5%88%99a13)
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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