Question

已知等比数列{an}中,a1=3,an=48,a(2n-3)=192,则满足|am|>2009的最小正整数m=?

Answer 1

an=a1*q^(n-1)=48 (i)

a(2n-3)=a1*q^(2n-4)=192 (ii)

（i)=>q^(n-1)=48/3=16 (iii)

(ii)/(i）=》q^(n-3)=192/48=4 (iv)

(iii)/(iv)=>q^2=4

=>|q|=2

|am|>2009

=>|a1*q^(m-1)|>2009

=>|q^(m-1)|>2009/3

又|q|=2

=>|q^9|=5122009/3

因此满足要求的最小m符合：m-1=10

=》m=11