Another way to solve this is to look at how the dot count grows from tile to tile instead of splitting the tiles into groups first, then confirm the jump into the answer using a second check.
Tile 1 to tile 2: dots go from 2 to 3, a rise of 1.
Tile 4 to tile 5: dots go from 6 to 10, a rise of 4. Since the tiles are not rising by a constant amount, the growth rate itself must be increasing, which is typical of a squared or "sum of small numbers" style rule rather than a simple addition rule.
Testing $n^2+1$ on the 1st, 3rd, 5th tiles: with $n=1,2,3$ this gives $2, 5, 10$. The 1st and 5th values (2 and 10) already match the tiles we can see, so the middle value, 5, is the strongest candidate for the missing tile.
Cross check with $n^2+2$ on the 2nd, 4th tiles: with $n=1,2$ this gives $3, 6$, which matches both visible tiles exactly, so the same style of rule is confirmed to be running on the other set of positions too.
Since both parallel rules check out against every tile we can actually see, the missing tile must carry $2^2+1=5$ dots.
