To continue the sequence of tiles shown, the tile indicated by the question mark should be: (The tiles in the sequence contain, in order, 0 dots, 1 dot, 1 dot, 2 dots, 3 dots, and 5 dots, followed by a tile marked with a question mark.)
Show Hint
Count the dots on each tile: 0, 1, 1, 2, 3, 5. This is the Fibonacci pattern, so the next tile needs 3 + 5 = 8 dots.
Step 1: Count the dots on each tile in order.
Write down how many dots appear on each tile from left to right: the first tile is blank (0 dots), the second has 1 dot, the third has 1 dot, the fourth has 2 dots, the fifth has 3 dots, and the sixth has 5 dots.
So the sequence of dot counts is: 0, 1, 1, 2, 3, 5.
Step 2: Find the rule linking one term to the next.
Check if each term is the sum of the two terms before it: 0 + 1 = 1 (matches the third term), 1 + 1 = 2 (matches the fourth term), 1 + 2 = 3 (matches the fifth term), 2 + 3 = 5 (matches the sixth term).
Every term equals the sum of the two terms right before it, so this is the Fibonacci pattern.
Step 3: Apply the rule to find the next term.
The next tile's dot count should equal the sum of the fifth and sixth terms: 3 + 5 = 8.
So the missing tile must show 8 dots.
Step 4: Match this count to the given options.
Option (A) shows 4 dots, option (B) shows 6 dots, option (C) shows 8 dots arranged in a ring, and option (D) shows 9 dots.
Only option (C) has exactly 8 dots, so it is the tile that continues the sequence correctly. Options (A), (B), and (D) show 4, 6, and 9 dots, none of which fit the required count of 8.
Final Answer:
The dot counts follow the Fibonacci rule 0, 1, 1, 2, 3, 5, 8, so the missing tile has 8 dots.
\[ \boxed{8 \text{ dots, option (C)}} \]
