Find the sum of the integers between $100$ and $200$ that are divisible by $9$.

The sum of the first $n$ terms of the $A.P.$ $-2, 1, 4, 7, \ldots$ 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.

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

For an $A.P.$,$a=11$ and $d=7$. Find the sum of the first $40$ terms of the $A.P.$

Can any term of the $A.P.$ $3, 7, 11, \ldots$ be $184$?