If $S_n$, the sum of first $n$ terms of an AP is given by $S_n=3n^2-4n$, find the $n^{\mathrm{th}}$ term.

If the sum of first four terms of an $\mathrm{AP}$ is $40$ and that of first $14$ terms is $280$. Find the sum of its first $\mathrm{n}$ terms.

Which term of the A.P $-\frac{11}{2}, -3, -\frac{1}{2}, ....\text{ is }\frac{49}{2}?$

Find $a and b$ so that the numbers $a, 7, b, 23$ are in A.P.