The $n^{th}$ term of the $A.P.$ $5, 10, 15, 20, \ldots$ is....... (in $n$)

Find the $12^{th}$ term of the $A.P.$ $9, 13, 17, 21, \ldots$

With respect to the usual notations of an $A.P.$,if $T_{n} = 4$,$d = 2$,and $S_{n} = -14$,find $n$ and $a$.

The sum of three consecutive terms of an $A.P.$ is $30$ and the product of its first and last term is $75$. Then,the common difference of the $A.P.$ is $\ldots \ldots \ldots \ldots .$

For an $A.P.$,the first term is $10$,the $n^{th}$ term is $40$,and the sum of the first $n$ terms is $150$. Find the value of $n$ and the common difference $d$.

For a given $A.P.$,the common difference is $5$ and its $15^{th}$ term is $72$. Find the first term of the $A.P.$ and its $50^{th}$ term.