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问题: 等差数列

已知两个等差数列{an}和{bn}的前n项和分别为Sn和Tn,且
Sn/Tn = (7n+1)/(4n+27),则a11/b11=?

解答:

等差数列中m+n=p+q则有am+an=ap+aq
由a11/b11=2a11/(2b11)
=(a1+a21)/(b1+b21)
=[21(a1+a21)/2]/[21(b1+b21)/2]
=S21/T21
=(7*21+1)/(4*21+27)
=148/111
=(4*37)/(3*37)
=4/3.