Analyze and extend the pattern of colored squares, where the side length is 2ⁿ and the total number of squares is (2ⁿ)2 = 2^(2n). Find the 3rd pattern.

Here are the extended patterns: 2. Extend the patterns. a) (Colored squares) Step 1: Analyze the pattern of colored squares. Pattern 1: A 2 × 2 square, total 4 small squares. Pattern 2: A 4 × 4 square, total 16 small squares. The side length of the square is 2ⁿ. The total number of small squares is (2ⁿ)² = 2²ⁿ. Step 2: Extend the pattern to the 3rd pattern. For the 3rd pattern (n=3): Side length = 2³ = 8. Total number of small squares $= 8 ×

Analyze and extend the pattern of colored squares, where the side length is 2ⁿ and the total number of squares is (2ⁿ)2 = 2^(2n). Find the 3rd pattern.

Here are the extended patterns: 2. Extend the patterns. a) (Colored squares) Step 1: Analyze the pattern of colored squares. Pattern 1: A 2 × 2 square, total 4 small squares. Pattern 2: A 4 × 4 square, total 16 small squares. The side length of the square is 2ⁿ. The total number of small squares is (2ⁿ)² = 2²ⁿ. Step 2: Extend the pattern to the 3rd pattern. For the 3rd pattern (n=3): Side length = 2³ = 8. Total number of small squares $= 8 ×

Solved: Analyze and extend the pattern of colored squares…

Here are the extended patterns:

2. Extend the patterns.

a) (Colored squares)

Analyze the pattern of colored squares.
- Pattern 1: A $2 \times 2$ square, total 4 small squares.
- Pattern 2: A $4 \times 4$ square, total 16 small squares. The side length of the square is $2^n$ . The total number of small squares is $(2^n)^2 = 2^{2n}$ .
Extend the pattern to the 3rd pattern.
For the 3rd pattern ( $n=3$ ):
Side length $= 2^3 = 8$ .
Total number of small squares $= 8 \times

Analyze and extend the pattern of colored squares, where the side length is 2ⁿ and the total number of squares is (2ⁿ)2 = 2^(2n). Find the 3rd pattern.

Step-by-step solution

Analyze the pattern of colored squares.

Extend the pattern to the 3rd pattern.

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