If ${S_n}$ denotes the sum of $n$ terms of an arithmetic progression, then the value of $({S_{2n}} - {S_n})$ is equal to

Find the sum to $n$ terms of the $A.P.,$ whose $k^{\text {th }}$ term is $5 k+1$

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

Let $3,7,11,15, \ldots, 403$ and $2,5,8,11, \ldots, 404$ be two arithmetic progressions. Then the sum, of the common terms in them, is equal to.....................

The sides of a triangle are distinct positive integers in an arithmetic progression. If the smallest side is $10$, the number of such triangles is

If the sum of the $10$ terms of an $A.P.$ is $4$ times to the sum of its $5$ terms, then the ratio of first term and common difference is