The first and last terms of an arithmetic progression are 7 and 43 respectively. The sum of the terms is 250. Find the number of terms and the common difference.

First term, $a = 7$
Last term, $l = 43$
Sum of the terms, $S_n = 250$

The formula for the sum of an arithmetic progression is:

Substitute the given values into the formula:

Divide by 25 to solve for $n$:

The number of terms in the progression is 10.

The formula for the $n$-th term (which is the last term $l$) is:

Substitute the known values $l=43$, $a=7$, and $n=10$:

Subtract 7 from both sides:

Divide by 9 to solve for $d$:

The common difference of the progression is 4.

The number of terms is $\boxed{10}$ and the common difference is $\boxed{4}$.