题目

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*.*a90等于多少

提问时间：2021-01-08

答案

a(n) = a2^(n-1),n = 1,2,...
2^30 = a(1)*a(2)*...*a(30) = a^30*2^[1 + 2 + ...+ 29] = a^30*2^[29*30/2],
a(3)*a(6)*...*a(90) = [a2^2]*[a2^5]*...*[a2^89] = a^30*2^[2 + 5 + ...+ 89)] = a^30*2^[(2+89)*30/2] = a^30*2^[29*30/2]*2^[62*30/2]
= 2^30*2^[31*30] = 2^[30*32] = 2^[960]