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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 stepsHere are the solutions for your geometric pattern problem:
- Extend the pattern by drawing stage 5.
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 dotsIdentify the rule.
Each stage adds one square and two dots to the previous stage.
For Stage 5, there will be 5 squares and 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.
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.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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