Question

已知数列{an}为等比数列,a3=16,a1a2...a10=2^65,求an

Answer 1

a1*a2*……*a10

=a1*(a1q)*……*(a1q^9)

=a1^10*q^(1+2+……+9)

=a1^10*q^45

=(a1^2*q^9)^5

=2^65

所以a^2*q^9=2^13 (1)

a3=a1*q^2=16

所以a1^2*q^4=256=2^8 (2)

(1)/(2)

q^5=2^5

q=2

a1=16/q^2=4

所以an=4*2^(n-1)=2^(n+1)