等差数列已知Sn.Tn分别是an,bn前n项和Sn/Tn=7n+2/n+3求a9/b9是Sn/Tn=(7n+2)/(n+3忘了加括号

Question

等差数列
已知Sn.Tn分别是an,bn前n项和
Sn/Tn=7n+2/n+3
求a9/b9
是Sn/Tn=(7n+2)/(n+3 忘了加括号

Answer 1

Sn=n(a1+an)/2
Tn=n(b1+bn)/2
已知Sn/Tn=(7n+2)/(n+3)
设Sn/Tn=(7n+2)/(n+3)=[(7n+2)x]/[(n+3)x]
Sn=(2n+1)x,Tn=(3n+1)x
a4=S4-S3=(7*4+2)x-(7*3+2)x=7x
b4=T4-T3=(1*4+3)x-(1*3+3)x=x
a4/b4=(S4-S3)/(T4-T3)=7x/x=7