If $2x, x + 8, 3x + 1$ are in $A.P.$,then the value of $x$ will be

If the sum of the first $n$ terms of an $A.P.$ is $cn(n - 1)$,where $c \neq 0$,then the sum of the squares of these terms is:

Let $a_1, a_2, a_3, \ldots$ be in an $A.P.$ such that $\sum_{k=1}^{12} a_{2k-1} = -\frac{72}{5} a_1$,where $a_1 \neq 0$. If $\sum_{k=1}^{n} a_k = 0$,then $n$ is:

The first term of an $A$.$P$. of $30$ non-negative terms is $\frac{10}{3}$. If the sum of this $A$.$P$. is the cube of its last term, then its common difference is:

Insert $6$ numbers between $3$ and $24$ such that the resulting sequence is an $A.P.$

Let the terms of an arithmetic progression be $a_1, a_2, a_3, \dots$. If $\frac{a_1 + a_2 + \dots + a_p}{a_1 + a_2 + \dots + a_q} = \frac{p^2}{q^2}$,where $p \neq q$,then $\frac{a_6}{a_{21}} = \dots$