If $a, b, c$ are in $A.P.$,then $(a + 2b - c)(2b + c - a)(c + a - b)$ equals

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.......

The sum of the first four terms of an $A.P.$ is $56$. The sum of the last four terms is $112$. If its first term is $11$,the number of terms is

If the $A.M.$ between $p^{th}$ and $q^{th}$ terms of an $A.P.$ is equal to the $A.M.$ between $r^{th}$ and $s^{th}$ terms of the same $A.P.$,then $p + q$ is equal to

If the $p^{th}$,$q^{th}$,and $r^{th}$ terms of an Arithmetic Progression are $a$,$b$,and $c$ respectively,then $[a(q - r) + b(r - p) + c(p - q)] = ?$

If $a_1, a_2, a_3, \dots, a_n$ are in an arithmetic progression with common difference $d$,then find the value of $\sin d [\csc a_1 \csc a_2 + \csc a_2 \csc a_3 + \dots + \csc a_{n-1} \csc a_n]$.