My view on such things is very simple:

   It doesn't relate to arithmetic progressions directly;

   It doesn't relate to geometric progressions directly;

   Hence, it doesn't relate to the school Math.

If it doesn't relate to the school Math, it has no connection with the purposes of this site.

Probably, it is a puzzle, and, probably, there are methods for their solutions, but it is totally different melody.

In my view, this site is not the appropriate place for such exercises.
Find another site  (they do exist)  and post such problems there.
Definitely, there are more appropriate sites for this.

Although other people can have the opposite view.