Math Problem Statement

Draw the 4th pattern in the sequence. How many squares in total are there in the 4th pattern?

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

  1. Each pattern forms an "L" shape made up of squares.
  2. 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: 9 (from Pattern 3)+3=12 squares.9 \text{ (from Pattern 3)} + 3 = 12 \text{ squares.}
    • 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:

  1. What is the general formula to find the number of squares in the nnth pattern?
  2. How does the sequence of blue squares alone progress?
  3. Can this pattern be related to an arithmetic sequence? If so, how?
  4. What is the difference between the growth in blue and orange squares in each step?
  5. 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