The $\ldots \ldots \ldots \ldots$th term of the $A.P.$ $8, 11, 14, 17, \ldots$ is $272$.

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: $1, 4, 9, 16, \ldots $

Two $AP$s have the same common difference. The first term of one of these is $-1$ and that of the other is $-8$. Then the difference between their $4^{\text{th}}$ terms is

For a given $A.P.$,the $5^{th}$ term is $20$ and the $10^{th}$ term is $35$. Find the sum of the first $20$ terms of this $A.P.$

Match the $APs$ given in column $A$ with suitable common differences given in column $B$.

Column $A$	Column $B$
$(A_{1}) \quad 2, -2, -6, -10, \ldots$	$(B_{1}) \quad \frac{2}{3}$
$(A_{2}) \quad a = -18, n = 10, a_{n} = 0$	$(B_{2}) \quad -5$
$(A_{3}) \quad a = 0, a_{10} = 6$	$(B_{3}) \quad 4$
$(A_{4}) \quad a_{2} = 13, a_{4} = 3$	$(B_{4}) \quad -4$
	$(B_{5}) \quad 2$
	$(B_{6}) \quad \frac{1}{2}$
	$(B_{7}) \quad 5$

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