How do you write a sequence that has three geometric means between 256 and 81?

1 Answer
Nov 20, 2015

256, 192, 144, 108, 81256,192,144,108,81

Explanation:

256=4^4256=44 and 81 = 3^481=34

So the geometric mean of 256256 and 8181 is:

sqrt(256*81) = sqrt(4^4*3^4) = 4^2*3^2 = 14425681=4434=4232=144

The geometric mean of 256256 and 144144 is:

sqrt(256*144) = sqrt(4^4 4^2 3^2) = 4^3*3 = 192256144=444232=433=192

The geometric mean of 144144 and 8181 is:

sqrt(144*81) = sqrt(4^2 3^2 3^4) = 4*3^3 = 10814481=423234=433=108

The sequence: 256, 192, 144, 108, 81256,192,144,108,81 is a geometric sequence with common ratio 3/434