In an arithmetic progression,the sum of the first and third terms is $12$,and the product of the first and second terms is $24$. Find the first term.

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 $a, b, c, d, e, f$ are in an arithmetic progression,then $e - c = \dots$

Let the arithmetic mean of $\frac{1}{a}$ and $\frac{1}{b}$ be $\frac{5}{16}$, where $a > 2$. If $\alpha$ is such that $a, 4, \alpha, b$ are in $A$.$P$.,then the equation $\alpha x^2 - ax + 2(\alpha - 2b) = 0$ has :

If the roots of $x^3+a x^2+b x+c=0$ are in arithmetic progression with common difference $1$,then

If the sum of $n$ terms of an $A.P.$ is $(pn + qn^2),$ where $p$ and $q$ are constants,find the common difference.