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 $a^2(b + c), b^2(c + a), c^2(a + b)$ are in Arithmetic Progression $(AP)$,then $a, b, c$ are in which progression?

If the first and $(2n - 1)^{th}$ terms of an $A.P.$,$G.P.$,and $H.P.$ are equal and their $n^{th}$ terms are respectively $a, b$ and $c$,then:

If the arithmetic mean between $p$ and $q$ $(p > q)$ is twice the geometric mean,then $p : q = .......$

If the ratio of the harmonic mean to the geometric mean of two positive numbers $a$ and $b$ $(a > b)$ is $4 : 5$,then $a : b = \dots$ (in $: 1$)

Consider two positive numbers $a$ and $b$. If the arithmetic mean of $a$ and $b$ exceeds their geometric mean by $\frac{3}{2}$ and the geometric mean of $a$ and $b$ exceeds their harmonic mean by $\frac{6}{5}$,then the absolute value of $(a^2 - b^2)$ is equal to