Answer:
1/4
Step-by-step 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
