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

Which of the following sequences is an $A.P.$?

Find the number of terms in the finite $A.P.$ $7, 11, 15, \ldots, 107$.

Find four numbers in $A.P.$ such that their sum is $36$ and the product of means ($2^{nd}$ and $3^{rd}$ term) exceeds the product of extremes ($1^{st}$ and $4^{th}$ term) by $32.$

The sum of the first $15$ terms of the $A.P.$ $-10, -12, -14, -16, \ldots$ is:

For the finite $A.P.$ $12, 21, 30, \ldots, 363,$ find the $12^{th}$ term from the end.