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The problem describes a geometric pattern. It involves squares and dots. The first stage has 1 square and 4 dots. The second stage has 2 squares and 6 dots. The third stage has 3 squares and 8 dots. T

Mathematics

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Step-by-step solution

5 steps

Here are the solutions for your geometric pattern problem:

  1. Extend the pattern by drawing stage 5.
  1. Observe the pattern for the number of squares and dots.

        *   Stage 1: 1 square, 4 dots
        *   Stage 2: 2 squares, 6 dots
        *   Stage 3: 3 squares, 8 dots
        *   Stage 4: 4 squares, 10 dots
    
  2. Identify the rule.

    Each stage adds one square and two dots to the previous stage.

  3. For Stage 5, there will be 5 squares and 10+2=1210 + 2 = 12 dots.

    *   **Drawing for Stage 5:**
        $$ \boxed{\text{
        \begin{tikzpicture}[scale=0.5]
        \draw (0,0) rectangle (1,1); \fill (0,0) circle (2pt); \fill (1,0) circle (2pt); \fill (0,1) circle (2pt); \fill (1,1) circle (2pt);
        \draw (1,0) rectangle (2,1); \fill (2,0) circle (2pt); \fill (2,1) circle (2pt);
        \draw (2,0) rectangle (3,1); \fill (3,0) circle (2pt); \fill (3,1) circle (2pt);
        \draw (3,0) rectangle (4,1); \fill (4,0) circle (2pt); \fill (4,1) circle (2pt);
        \draw (4,0) rectangle (5,1); \fill (5,0) circle (2pt); \fill (5,1) circle (2pt);
        \end{tikzpicture}
        }} $$
    

    2. Describe the general rule or observed relationships in own words.

  4. Analyze how the pattern changes from one stage to the next.

        *   The number of squares increases by one in each subsequent stage.
        *   The number of dots increases by two in each subsequent stage.
    
  5. Formulate a description based on these observations.

    *   Rule: $\boxed{\text{The pattern starts with one square and four dots. For each new stage, one square is added to the right, which increases the total number of dots by two.}}$
    
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