The correct answer to this question is A, 64. To find a geometric mean, the current ratio must first be found. Symbolized by the variable r, the common ratio is the constant between the numbers provided. The equation r squared n-1 = an/ a1.

Plugging in the information we have been given, and the equation turns into r 5-1 equals 256/1. 5-1 equals four, and 256 divided by 1 are 256. This makes r4 = 256. Then, we would square root 256 by 4, which equals 4 or r = 4. So, with knowing 4, and inserting three geometric means between 1 and 256, the third would be 64. 1, ____, ____, ____, 256 or 1, 4, 16, 64, 256.