Which of the following is not an $A.P.$?

Find the sum of the first $25$ terms of the $A.P.$ $3, \frac{9}{2}, 6, \frac{15}{2}, \ldots$

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.

Find whether $55$ is a term of the $AP: 7, 10, 13, \dots$ or not. If yes, find which term it is. (in $^{th}$)

Which term of the $A.P.$ $13, 20, 27, 34, \ldots$ is $384$ (in $^{th}$)?

In each of the following,$a$ and $d$ for an $A.P.$ are given. Find the $A.P.$ in each case. $a = -12, d = 3$.