The first term of an $A.P.$ is denoted by $\ldots \ldots \ldots \ldots .$

Determine whether the following sequence is an $A.P.$ or not. (Assume that the pattern continues.) If it is an $A.P.$,find its $n^{th}$ term: $\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \ldots$

The taxi fare after each $km$,when the fare is $Rs. 15$ for the first $km$ and $Rs. 8$ for each additional $km$,does not form an $AP$ as the total fare (in $Rs.$) after each $km$ is $15, 8, 8, 8, \ldots$. Is the statement true? Give reasons.

If $2x$,$x+10$,and $3x+2$ are three consecutive terms of an $A.P.$,find the value of $x$.

Write the first four terms of the $AP,$ when the first term $a$ and the common difference $d$ are given as follows: $a = -2, d = 0.$

The sum of three numbers in $A.P.$ is $12$ and the sum of their cubes is $288$. Find those numbers.