Let $S_n$ denote the sum of the first $n$ terms of an $A.P$.. If $S_4 = 16$ and $S_6 = -48$, then $S_{10}$ is equal to

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

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

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

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

If ${a_1},\;{a_2},............,{a_n}$ are in $A.P.$ with common difference , $d$, then the sum of the following series is $\sin d(\cos {\rm{ec}}\,{a_1}.co{\rm{sec}}\,{a_2} + {\rm{cosec}}\,{a_2}.{\rm{cosec}}\,{a_3} + ...........$$ + {\rm{cosec}}\;{a_{n - 1}}{\rm{cosec}}\;{a_n})$