Find the $100^{th}$ term of the $A.P.$ $50, 56, 62, 68, \ldots$

Find the sum of the series: $3 + 7 + 11 + \ldots + 119$.

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

The sequence $1, 3, 6, 10, \ldots$ is

The first term of an $AP$ is $-5$ and the last term is $45$. If the sum of the terms of the $AP$ is $120$,then find the number of terms and the common difference.

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?