If $a, b, c$ are in $AP$,and $b-a, c-b, a$ are in $GP$,then $a: b: c$ is

If the $A.M.$,$G.M.$,and $H.M.$ between two positive numbers $a$ and $b$ are equal,then

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

If $A$ and $G$ are the arithmetic mean and geometric mean of $a$ and $b$ respectively,then what is the value of $A - G$?

In a $G.P.$,the sum of three numbers is $14$. If $1$ is added to the first two numbers and subtracted from the third number,the series becomes an $A.P.$. Then,the greatest number is:

Three positive numbers form an increasing $G.P.$ If the middle term in this $G.P.$ is doubled,the new numbers are in $A.P.$ Then the common ratio of the $G.P.$ is: