If the sum of three numbers in an $A.P.$ is $24$ and their product is $440,$ find the numbers.

If $a_1, a_2, \dots, a_n$ are positive real numbers such that their product is a constant $c$,then what is the minimum value of $a_1 + a_2 + \dots + a_{n-1} + 2a_n$?

If $\frac{S_n}{S_m} = \frac{n^4}{m^4}$ (where $S_k$ is the sum of the first $k$ terms of an $A$.$P$. $a_1, a_2, \dots$),then the value of $\frac{a_{m+1}}{a_{n+1}}$ in terms of $m$ and $n$ is:

The sum of $n$ terms of an arithmetic progression is $nA + n^2B$,where $A$ and $B$ are constants. The common difference of this progression is.......

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

Let $S_{1}$ be the sum of the first $2n$ terms of an arithmetic progression. Let $S_{2}$ be the sum of the first $4n$ terms of the same arithmetic progression. If $(S_{2} - S_{1})$ is $1000$,then the sum of the first $6n$ terms of the arithmetic progression is equal to: