With respect to the usual notations of an $A.P.$,if $a=3, n=8$ and $S_{n}=192$,find the common difference $d$.

Can any term of the $A.P.$ $14, 18, 22, \ldots$ be $142$? If yes,which term?

The sum of the first $n$ terms of the $A.P.$ $-2, 1, 4, 7, \ldots$ is:

The sum of the first five terms of an $AP$ and the sum of the first seven terms of the same $AP$ is $167$. If the sum of the first ten terms of this $AP$ is $235$,find the sum of its first twenty terms.

The $15^{th}$ term of the $A.P.$ $1, 11, 21, 31, \dots$ is........

The sum of the first $n$ terms of an $A.P.$ is given by $S_{n} = \ldots \ldots \ldots \ldots$