The first two terms in an arithmetic progression are $146$ and $139$. The last term is $-43$. Find the sum of all the terms in this progression.

The first term of an arithmetic progression is $2$ and the ${11}^{\mathrm{th}}$ term is $17$. The sum of all the terms in the progression is $500$. Find the number of terms in the progression.

The sixth term of an arithmetic progression is $-3$ and the sum of the first ten terms is $-10$. Find the first term and the common difference.

The sixth term of an arithmetic progression is $-3$ and the sum of the first ten terms is $-10$. Given that the ${\mathrm{n}}^{\mathrm{th}}$ term of this progression is $-59$, find the value of $\mathrm{n}$.
 

The sum of the first terms, S_n, of a particular arithmetic progression is given by ${\mathrm{S}}_{\mathrm{n}}= 4{\mathrm{n}}^2+3\mathrm{n}$. Find the first term and the common difference.