Determine $k,$ so that $k+2, 4k-6$ and $3k-2$ are three consecutive terms of an $A.P.$

If the $10^{\text{th}}$ term of an $A$.$P$. is $\frac{1}{20}$ and its $20^{\text{th}}$ term is $\frac{1}{10}$,then the sum of its first $200$ terms is

If the $m^{th}$ term of a $H.P.$ is $n$ and the $n^{th}$ term is $m$,then the $r^{th}$ term will be

The $7^{th}$ term of an $A.P.$ is $40$,then the sum of the first $13$ terms is:

The sum of $n$ arithmetic means between $a$ and $b$ is:

If $\alpha, \beta, \gamma$ are the geometric means between $ca, ab$; $ab, bc$; and $bc, ca$ respectively,where $a, b, c$ are in $A.P.$,then $\alpha^2, \beta^2, \gamma^2$ are in