The formula to find the $n^{th}$ term of an $A.P.$ is $\ldots \ldots \ldots \ldots .$

To clear a debt,Ajaybhai has to pay $Rs. 100$ in the first monthly instalment,$Rs. 150$ in the second monthly instalment,and onwards he has to pay in each monthly instalment $Rs. 50$ more than what was paid in the previous instalment. He has to pay $24$ monthly instalments in all. What amount will he pay in the $24^{th}$ instalment?

Find the number of terms in the finite $A.P.$ $6, 5.5, 5, \ldots, -12$.

The sum of the $4^{th}$ and $8^{th}$ terms of an $AP$ is $24$ and the sum of the $6^{th}$ and $10^{th}$ terms is $44$. Find the first three terms of the $AP$.

The $20^{th}$ term of an $A.P.$ is $40$ and the common difference is $2$. Then,its second term is $\ldots \ldots \ldots \ldots$

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: $1.4, 2.3, 3.2, 4.1, \dots$