The sum of $n$ terms of an $A.P.$ is given by $S_{n} = 2n^{2} + 5n$. Then,the $n^{th}$ term of the $A.P.$ $T_{n} = \dots$

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 $

Write the first three terms of the $APs$ when $a$ and $d$ are as given below:
$a = \frac{1}{2}, d = -\frac{1}{6}$

For the finite $A.P.$ $40, 35, 30, \ldots, -200,$ find the $10^{th}$ term from the end.

The sum of four numbers in $A.P.$ is $50$. The greatest number is four times the smallest number. Find those numbers.

For the $A.P.$ $-2, -4, -6, \ldots,$ the common difference $d = \ldots$