341. Find the condition under which the sum of any two terms of an arithmetic progression represents a term of the same progression.
Instruction. According to the condition of the problem, we should have:

$$
(a+d n)+(a+d k)=a+d p
$$

where $a$ is the first term of the progression, $d$ is the common difference of the progression, and $n, p, k$ are positive integers. Then $a=d(p-k-n)$, i.e., the first term of the progression must be a multiple of the common difference of the progression.

Note. In problems $342-346$, the relationship between three consecutive terms of an arithmetic progression should be used.