In the sequence of tiles shown below, the missing tile indicated by the question mark should be
Show Hint
Count the dots in each tile of the sequence and look for a pattern connecting consecutive tiles, such as each tile's count being the sum of the previous two.
Step 1: Count the dots in each known tile.
The first tile has \(2\) dots, the second tile has \(3\) dots. The fourth tile (right after the missing one) and the fifth tile have larger dot counts, and the fifth tile clearly has the most dots of all five tiles.
Step 2: Look for the rule linking one tile to the next.
Test whether each tile's dot count is simply the sum of the two tiles before it, a common rule in this kind of visual number sequence (the same rule behind the Fibonacci sequence \(1, 1, 2, 3, 5, 8, 13, \ldots\)). Starting from \(2\) and \(3\):
\[ 2, \ 3, \ 2+3=5, \ 3+5=8, \ 5+8=13 \]
This gives the sequence \(2, 3, 5, 8, 13\), which matches the visual jump in dot density from the first two small tiles up to the last, most crowded tile.
Step 3: Identify the missing tile.
Since the missing tile sits in the third position, its dot count must be \(2+3=5\). So the correct tile must show exactly \(5\) dots.
Step 4: Match against the options.
Option (A) shows \(4\) dots in a square, which does not equal \(5\), so it is ruled out. Option (B) shows \(5\) dots arranged with one dot in the middle and two on each side, matching the required count of \(5\) exactly. Option (C) and option (D) both show \(6\) dots, which is one too many, so both are ruled out.
Step 5: Final answer.
The missing tile must contain \(5\) dots, so option (B) is correct.
\[ \boxed{\text{Option (B): 5 dots}} \]
