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

$A$ class has $49$ students who are allotted roll numbers from $1$ to $49$. Find a roll number $n$ such that the sum of all the roll numbers smaller than $n$ is equal to the sum of all the roll numbers greater than $n$.

There are $\ldots \ldots \ldots \ldots$ terms in the finite $A.P.$ $5, 10, 15, \ldots, 200$.

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?

The sum of the first $16$ terms of the $A.P.$ $1, 1.5, 2, \ldots$ is:

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