The number of terms in the series $101 + 99 + 97 + \dots + 47$ is

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

Let $S_{n}$ denote the sum of the first $n$ terms of an arithmetic progression. If $S_{10} = 530$ and $S_{5} = 140$,then $S_{20} - S_{6}$ is equal to:

If the first term of an $A.P.$ is $3$ and the sum of its first $25$ terms is equal to the sum of its next $15$ terms,then the common difference of this $A.P.$ is:

Let $a_1, a_2, a_3, \ldots$ be terms of an $A.P.$ If $\frac{a_1 + a_2 + \ldots + a_p}{a_1 + a_2 + \ldots + a_q} = \frac{p^2}{q^2}$ for $p \ne q$,then $\frac{a_6}{a_{21}}$ equals:

If $a, b, c$ are in $A.P.$,then $\frac{(a - c)^2}{(b^2 - ac)} = $