Question

The GM of a series of a three positive numbers is 4 by including fourth number it becomes 2 what is fourth value

Answer 1

1/4

Explanation:

Let a₁, a₂, a₃ and a₄ be the four numbers. Since the geometric mean of the first 3 positive numbers is 4, we have that

∛(a₁a₂a₃) = 4. (1)

Also the geometric mean of the four numbers is 2, we have that ⁴√(a₁a₂a₃a₄) = 2 (2).

So, taking the cube of (1), we have

[∛(a₁a₂a₃)]³ = 4³

a₁a₂a₃ = 64 (3)

Also, taking the fourth power of equation (2), we have

[⁴√(a₁a₂a₃a₄)]⁴ = 2⁴

a₁a₂a₃a₄ = 16 (4)

Dividing (4) by (3), we have

a₁a₂a₃a₄/a₁a₂a₃ = 16/64

a₄ = 1/4

The fourth value is 1/4