Question

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

Answer 1

方法一(2n-1)an=S(2n-1),

(2n-1)bn=T(2n-1),

所以an/bn=S(2n-1)/T(2n-1)

=[7(2n-1)+1]/[4(2n-1)+27]

=(14n-6)/(8n+23) 方法二因为等差数列前N项和形式是xN^2+yN

所以 An = 7n^2+n(真正形式,未约分前）

Bn= 4n+27 (真正形式,未约分前）

所以an = 8+ 14*(n-1)=14n-6

bn = 31 + 8*(n-1)=8n+23

an/bn=(14n-6)/(8n+23