Which of the following is an $A.P.$?

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

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: $5, 11, 17, 23, \ldots$

Which term of the $A.P.$ $13, 20, 27, 34, \ldots$ is $384$ (in $^{th}$)?

The $11^{\text{th}}$ term of the $AP: -5, \frac{-5}{2}, 0, \frac{5}{2}, \dots$ is

Jaspal Singh repays his total loan of $Rs. 118000$ by paying every month starting with the first instalment of $Rs. 1000$. If he increases the instalment by $Rs. 100$ every month,what amount will be paid by him in the $30^{\text{th}}$ instalment? What amount of loan does he still have to pay after the $30^{\text{th}}$ instalment?