If $\frac{1}{{b – c}},\;\frac{1}{{c – a}},\;\frac{1}{{a – b}}$ be consecutive terms of an $A.P.$, then ${(b – c)^2},\;{(c – a)^2},\;{(a – b)^2}$ will be in

Maximum value of sum of arithmetic progression $50, 48, 46, 44 ……..$ is :-

A series whose $n^{th}$ term is $\left( {\frac{n}{x}} \right) + y,$ the sum of $r$ terms will be

Let the sum of the first three terms of an $A. P,$ be $39$ and the sum of its last four terms be $178.$ If the first term of this $A.P.$ is $10,$ then the median of the $A.P.$ is

Let $AP ( a ; d )$ denote the set of all the terms of an infinite arithmetic progression with first term a and common difference $d >0$. If $\operatorname{AP}(1 ; 3) \cap \operatorname{AP}(2 ; 5) \cap \operatorname{AP}(3 ; 7)=\operatorname{AP}( a ; d )$ then $a + d$ equals. . . . .