Question

设由正数组成的等比数列,公比q=2,且a1*a2.*a30=2^30,则a3*a6*a9*.*a30等于多少?

Answer 1

an=a1*q^(n-1)

设x=a1*a2*...*a30= a1^30*q^[0+1+2+3+...+29]

=a1^30*2^435

设y=a3*a6*...*a30=a1^10 * q^(2+5+8+...+29)

=a1^10 * 2^155

y^3=a1^30 * 2^ 465 =a1^30*2^435*2^30

=x*2^30

x=2^30

y^3=2^30*2^30=2^60 ==> y=2^20

a3·a6·a9.a30=2^20