Let $A_1, G_1, H_1$ be the arithmetic,geometric,and harmonic means of two distinct positive numbers. For $n \geq 2$,let $A_n, G_n, H_n$ be the arithmetic,geometric,and harmonic means of $A_{n-1}$ and $H_{n-1}$ respectively. Which of the following statements is true?

• A
  $A_1 > A_2 > A_3 > \dots$
• B
  $A_1 < A_2 < A_3 < \dots$
• C
  $A_1 > A_3 > A_5 > \dots$ and $A_2 < A_4 < A_6 < \dots$
• D
  $A_1 < A_3 < A_5 < \dots$ and $A_2 > A_4 > A_6 > \dots$