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}} = $
$909$
$75$
$750$
$900$
Insert $6$ numbers between $3$ and $24$ such that the resulting sequence is an $A.P.$
The sum of all two digit numbers which, when divided by $4$, yield unity as a remainder is
Find the $25^{th}$ common term of the following $A.P.'s$
$S_1 = 1, 6, 11, .....$
$S_2 = 3, 7, 11, .....$
If $n$ arithmetic means are inserted between a and $100$ such that the ratio of the first mean to the last mean is $1: 7$ and $a+n=33$, then the value of $n$ is
The mean of the series $a,a + nd,\,\,a + 2nd$ is