2024 · Q42
Let the positive numbers a₁, a₂, a₃, …, a₃ₙ be in GP. If P is the GM of a₁, a₂, a₃, ...., aₙ and Q is the GM of aₙ₊₁, aₙ₊₂, aₙ₊₃, …, a₃ₙ, then what is the GM of 3n numbers?
Elementary MathematicsNumber System
- AP²Q
- BPQ²
- CPQ
- Dp¹/3 Q²/3
Explanation
Pⁿ is the product a₁⋯aₙ and Q²ⁿ is the product aₙ₊₁⋯a₃ₙ. The GM of all 3n terms is therefore (PⁿQ²ⁿ)^{1/3n} = P^{1/3}Q^{2/3}. Hence the answer is option (d).