For the finite $A.P.$ $40, 35, 30, \ldots, -200,$ find the $10^{th}$ term from the end.

In which of the following situations,do the lists of numbers involved form an $AP$? Give reasons for your answers.
$(i)$ The fee charged from a student every month by a school for the whole session,when the monthly fee is $Rs. 400$.
$(ii)$ The fee charged every month by a school from Classes $I$ to $XII$,when the monthly fee for Class $I$ is $Rs. 250$,and it increases by $Rs. 50$ for the next higher class.
$(iii)$ The amount of money in the account of Varun at the end of every year when $Rs. 1000$ is deposited at simple interest of $10\%$ per annum.
$(iv)$ The number of bacteria in a certain food item after each second,when they double in every second.

For the $A.P.$ $4, 8, 12, 16, \ldots$,$T_{40} - T_{30} = \ldots$

The sum of the first $n$ terms of an $A.P.$ is given by $S_{n} = 7n^{2} - 3n$. Find the $n^{th}$ term of the $A.P.$

Which term of the $A.P.$ $-1, 3, 7, 11, \ldots$ is $95$ (in $^{th}$)?

For an $A.P.$,the $12^{th}$ term is $4$ and the $20^{th}$ term is $-20$. Find the $n^{th}$ term of the $A.P.$