The $n^{th}$ term of an $A.P.$ is given by $T_{n} = 3n - 1$. Then,the common difference of the $A.P.$ is ...........

The sum of the first $20$ terms of the $A.P.$ $5, 11, 17, 23, \ldots$ is:

If $S_{n}$ denotes the sum of the first $n$ terms of an $AP$,prove that $S_{12} = 3(S_{8} - S_{4})$.

Determine whether the following sequence is an $A.P.$ or not. (Assume that the pattern continues.) If it is an $A.P.$,find its $n^{th}$ term: $\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \ldots$

For the $A.P.$ $0.1, 0.4, 0.7, 1, \ldots,$ the common difference is.........

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 $d$.