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

Find the sum of the first $30$ terms of the $A.P.$ $15, 20, 25, \ldots$

If the sum of the first $n$ terms of an $AP$ is $4n - n^2$,what is the first term (that is $S_1$)? What is the sum of first two terms? What is the second term? Similarly,find the $3^{rd}$,the $10^{th}$ and the $n^{th}$ terms.

The sum of the first $n$ terms of an $AP$ whose first term is $8$ and the common difference is $20$ is equal to the sum of first $2n$ terms of another $AP$ whose first term is $-30$ and the common difference is $8$. Find $n$.

For an $A.P.$,the $5^{th}$ term is $30$ and the $12^{th}$ term is $100$. Find the sum of the first $20$ terms of the $A.P.$

For an $A.P.$,$T_{n} = \ldots \ldots \ldots \ldots (n > 1)$