If sum of first $6$ terms of an AP is $36$ and that of the first $16$  terms is $256$, then first find the sum of first $10$ terms.

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.

The sum of the first $7$ terms of an AP is $182$. If its $4^{\mathrm{th}}$ and ${17}^{\mathrm{th}}$ terms are in the ratio $1:5$, find the AP.