Find the sum of first $51$ terms of an AP whose second and third terms are $14$ and $18$ respectively.

Find an A.P. whose fourth term is $9$ and the sum of its sixth and thirteenth terms is $40$.

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.