Split $207$ into three parts such that these are in $AP$ and the product of the two smaller parts is $4623$.

There are $\ldots \ldots \ldots \ldots$ terms in the finite $A.P.$ $5, 10, 15, \ldots, 200$.

Find the $n^{th}$ term of the $A.P. \, 6.4, 7.6, 8.8, 10, \ldots$

$A$ plastic toy consists of $14$ circular discs of different radii. The radius of the smallest disc is $1\, cm$, the radius of the next bigger disc is $2\, cm$, and so on, such that the radius of the biggest disc is $14\, cm$. Find the sum of the circumferences of all the discs in $cm$.

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 number of terms in the finite $A.P.$ $13, 26, 39, \ldots, 650$ is ........