已知等比数列{an}中,a1－a3＋5＝2,a3－a5＋a7＝5,那么a5－a7＋9＝?

Question

已知等比数列{an}中,a1－a3＋5＝2,a3－a5＋a7＝5,那么a5－a7＋9＝?

Answer 1

a1-a3+a5=2,
a3-a5+a7=5
两式相除得
(a3-a5+a7)/(a1-a3+a5)=5/2
(a1q^2-a3q^2+a5q^2)/(a1-a3+a5)=5/2
q^2(a1-a3+a5)/(a1-a3+a5)=5/2
q^2=5/2
令a5-a7+a9=k
a3-a5+a7=5,
a5-a7+a9=k
两式相除得
(a5-a7+a9)/(a3-a5+a7)=k/5
(a3q^2-a5q^2+a7q^2)/(a3-a5+a7)=k/5
q^2(a3-a5+a7)/(a3-a5+a7)=k/5
q^2=k/5
k=5q^2
k=5*5/2
k=25/2
所以a5-a7+a9=25/2