Question

在等比数列{an}中,a6×a8=16×a4,a9=4,求an

Answer 1

a9=a4q^5=4 a4=4/q^5

a6×a8=a4q^2×a4q^4=(a4q^3)^2=(4×q^3/q^5)^2=16/q^4=16×a4

a4q^4=a8=1

q=a9/a8=4/1=4

a1=a9/q^8=4/4^8=4^(-7)

an=a1q^(n-1)=4^(-7)×4^(n-1)=4^(n-8)