If the sum of $n$ terms of an arithmetic progression is $2n^2 + 5n$,then its $n^{th}$ term is.........

If for an Arithmetic Progression $(AP)$,$9$ times the $9^{th}$ term is equal to $13$ times the $13^{th}$ term,then the value of the $22^{nd}$ term is:

If $a + 2b + 3c = 6$,then the greatest value of $abc^2$ is (where $a, b, c$ are positive real numbers).

The solution of the equation $(x + 1) + (x + 4) + (x + 7) + \dots + (x + 28) = 155$ 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 arithmetic mean of the nine numbers in the given set $\{9, 99, 999, \dots, 999999999\}$ is a $9$-digit number $N$,all whose digits are distinct. The number $N$ does not contain the digit: