If the sides of a right-angled triangle are in $A.P.$,then their ratio is:

If the sum of three consecutive terms of an $A.P.$ is $51$ and the product of the last and first term is $273$,then the numbers are

If $p$ times the $p^{th}$ term of an arithmetic progression is equal to $q$ times its $q^{th}$ term,then the $(p + q)^{th}$ term of this progression is........

If ${a_1}, {a_2}, ..., {a_n}$ are positive real numbers whose product is a fixed number $c$,then the minimum value of ${a_1} + {a_2} + ... + {a_{n-1}} + 2{a_n}$ is

$150$ workers were engaged to finish a job in a certain number of days. $4$ workers dropped out on the second day,$4$ more workers dropped out on the third day,and so on. It took $8$ more days to finish the work. Find the number of days in which the work was completed.

If ${a_1}, {a_2}, {a_3}, \dots, {a_{24}}$ 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} + \dots + {a_{23}} + {a_{24}} = $