The sum of the first $16$ terms of the $AP: 10, 6, 2, \ldots$ is

The $\ldots \ldots \ldots \ldots^{th}$ term of the $A.P.$ $200, 196, 192, \ldots$ is $0$.

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

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.

If $k+1, 8, k+9$ are three consecutive terms of an $A.P.$,then $k = \ldots$

For a given $A.P.$,the common difference is $5$ and its $15^{th}$ term is $72$. Find the first term of the $A.P.$ and its $50^{th}$ term.