The sum of the first $n$ terms of an $A.P.$ is given by $S_{n} = 3n^{2} + 5n$. Find the $n^{th}$ term of the $A.P.$

(N/A) The $n^{th}$ term of an $A.P.$ is given by the formula $a_{n} = S_{n} - S_{n-1}$ for $n > 1$.
Given $S_{n} = 3n^{2} + 5n$.
Then $S_{n-1} = 3(n-1)^{2} + 5(n-1) = 3(n^{2} - 2n + 1) + 5n - 5 = 3n^{2} - 6n + 3 + 5n - 5 = 3n^{2} - n - 2$.
Now,$a_{n} = (3n^{2} + 5n) - (3n^{2} - n - 2) = 3n^{2} + 5n - 3n^{2} + n + 2 = 6n + 2$.
For $n = 1$,$a_{1} = S_{1} = 3(1)^{2} + 5(1) = 8$.
Thus,the $n^{th}$ term is $a_{n} = 6n + 2$ for $n \geq 1$.