Sequences And Series

Let \(\mathrm{A_{1}, G_{1}}, \mathrm{H}_{1}\) denote the arithmetic, geometric and harmonic means, respectively, of two distinct positive numbers. For \(n \geq 2\), let \(\mathrm{A}_{n-1}\) and \(\mathrm{H}_{n-1}\) have arithmetic, geometric and harmonic means as \(\mathrm{A_{n}}\), \(\mathrm{G}_{\mathrm{n}}, \mathrm{H}_{\mathrm{n}}\) respectively.

Which one of the following statements is correct?