Question

Write the ratio that can be used to calculate the geometric mean of 6 and 42

Answer 1

Gm = √a*b  for two numbers
hence gm = √6*42 = 2√63 = 15.87 

Answer 2

Geometric mean of 6 and 42

Since the number of terms = 2

So we take the second root of (6*42)

Geometric mean = √(6*42) ≈ 15.8745

So the number 15.8745 is between 6 and 42.

So the geometric series is....   6, 15.8745, 42

So the geometric ratio =  15.8745/6

                                        ≈ 2.646

Geometric ratio   ≈ 2.646

Hence Geometric mean ≈ 15.8745,  Geometric ratio ≈ 2.646

Hope this helps.