If ${a_1},\;{a_2},\,{a_3},……{a_{24}}$ are in arithmetic progression and ${a_1} + {a_5} + {a_{10}} + {a_{15}} + {a_{20}} + {a_{24}} = 225$, then ${a_1} + {a_2} + {a_3} + …….. + {a_{23}} + {a_{24}} = $

The sum of all those terms, of the anithmetic progression $3,8,13, \ldots \ldots .373$, which are not divisible by $3$,is equal to $…….$.

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})$

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

The sum of all natural numbers between $1$ and $100$ which are multiples of $3$ is