If $a, b, c$ are in $A.P.$ and $b, c, d$ are in $H.P.$,then

If $a, b, c$ are three unequal numbers such that $a, b, c$ are in $A.P.$ and $b - a, c - b, a$ are in $G.P.$,then $a : b : c$ is

If $\frac{a + b}{1 - ab}, b, \frac{b + c}{1 - bc}$ are in $A.P.$,then $a, \frac{1}{b}, c$ are in

The number of terms common between the two series $2 + 5 + 8 + \dots$ up to $50$ terms and the series $3 + 5 + 7 + 9 + \dots$ up to $60$ terms is:

The geometric mean of two numbers is $6$ and their arithmetic mean is $6.5$. The numbers are

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?