Subjects algebra

Pattern Rule F888A5

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Pattern Rule F888A5


1. The problem states: Start with 2 blue circles and 1 red square, then add 4 red squares each time. 2. We want to find the pattern rule for the number of red squares in each step. 3. Let $n$ be the step number (starting at 1). 4. The initial number of red squares at step 1 is 1. 5. Each subsequent step adds 4 red squares, so the number of red squares at step $n$ is given by the arithmetic sequence formula: $$\text{Red squares} = 1 + 4(n-1)$$ 6. Simplify the formula: $$1 + 4n - 4 = 4n - 3$$ 7. Check the first few values: - Step 1: $4(1) - 3 = 1$ red square - Step 2: $4(2) - 3 = 5$ red squares - Step 3: $4(3) - 3 = 9$ red squares 8. Now, compare this with the two graphs: - Top-right graph shows red squares as 1, 3, 5 (increments of 2) - Bottom-right graph shows red squares as 2, 4, 6 (increments of 2) Neither matches the pattern of adding 4 red squares each time starting from 1. 9. Since the problem states adding 4 red squares each time starting from 1, the correct pattern should be 1, 5, 9, ... red squares. 10. Therefore, neither graph matches the pattern rule exactly, but the top-right graph starts with 1 red square and increases, though by 2 each time, not 4. Final answer: The correct pattern rule for red squares is $$\boxed{4n - 3}$$, which corresponds to starting with 1 red square and adding 4 each time. The top-right graph does not match this rule, nor does the bottom-right graph. Hence, neither graph shows the correct pattern for the given rule.