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

In each of the following,$a$ and $d$ for an $A.P.$ are given. Find the $A.P.$ in each case. $a = -15, d = -7$.

If the sum of the first $6$ terms of an $AP$ is $36$ and that of the first $16$ terms is $256,$ find the sum of the first $10$ terms.

For the $A.P.$ $3, 13, 23, 33, \ldots,$ its $\ldots \ldots \ldots \ldots$ term exceeds its $21^{st}$ term by $10.$

For an $A.P.$,the $5^{th}$ term is $30$ and the $12^{th}$ term is $100$. Find the sum of the first $20$ terms of the $A.P.$

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: $\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \ldots$