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Let \( A_{1}, G, H_{1} \) denote the arithmetic, geometric and harmonic means respectively, of two distinct positive numbers. For \( n2 \), let \( A_{n-1} \) and \( H_{n-1} \) have arithmetic, geometric and harmonic means as \( A_{n}, G_{n}, H_{n} \) respectively. Then, which one of the following statements is correct?
(A) \( G_{1}G_{2}G_{3}\ldots \)
(B) \( GG_{2}G_{3}\ldots \)
(C) \( G_{1}=G_{2}=G_{3}=\ldots \)
(D) \( G_{1}G_{3}G_{5} \ldots \) and \( G_{2}G_{4}G_{6}\ldots \)
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