Math Problem Statement
Solution
From the provided image, we can analyze the sequence of patterns to solve the question. Here’s how to approach it:
Observing the Pattern
- Each pattern forms an "L" shape made up of squares.
- The number of squares increases as the pattern progresses:
- Pattern 1: 3 squares (2 blue, 1 orange)
- Pattern 2: 6 squares (5 blue, 1 orange)
- Pattern 3: 9 squares (8 blue, 1 orange)
Rule for Adding Squares
- Between consecutive patterns, 3 squares are added each time to the previous total. The orange square remains constant, and blue squares increase.
Calculating for the 4th Pattern
- Number of squares in Pattern 4:
- This includes 11 blue squares and 1 orange square.
Final Answer
- Total squares in the 4th pattern: 12 squares.
Would you like a detailed explanation of how to draw the pattern? Let me know!
Related Questions:
- What is the general formula to find the number of squares in the th pattern?
- How does the sequence of blue squares alone progress?
- Can this pattern be related to an arithmetic sequence? If so, how?
- What is the difference between the growth in blue and orange squares in each step?
- If there were a 10th pattern, how many squares would it contain?
Tip:
Always look for consistent growth or changes in a sequence to establish a mathematical rule or formula!
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Math Problem Analysis
Mathematical Concepts
Arithmetic Sequences
Pattern Recognition
Basic Algebra
Formulas
n = a + (k-1)d (Arithmetic sequence formula)
Theorems
Arithmetic Sequence Properties
Suitable Grade Level
Grade 6-8
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