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4. Complete all parts of the following growing pattern problem Draw the next two shapes in the pattern. If you count the shaded square too, how many squares will be in the 10th shape. In the 25th shape? How many squares will be in the nth shape?

4. Complete all parts of the following growing pattern problem Draw the next two shapes in the pattern. If you count the shaded square too, how many squares will be in the 10th shape. In the 25th shape? How many squares will be in the nth shape?

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Title: Growing Pattern Problem** **Objective:** Comprehend the pattern and extend it to predict the number of squares in specified position. **Instructions:** 1. **Task:** Draw the next two shapes in the pattern provided. 2. **Pattern Recognition:** Study the given shapes and identify the pattern of growth. **Illustration:** - The figure showcases three shapes arranged in a sequential pattern: - The 1st shape has 5 squares forming a plus sign with a shaded square in the center. - The 2nd shape has 9 squares arranged in a larger plus sign with 1 square added to each arm of the previous plus sign. The center square remains shaded. - The 3rd shape has 13 squares forming an even larger plus sign with 1 additional square appended to each extended arm from the previous shape. The center square stays shaded. 3. **Extension Questions:** - **Determine the number of squares in future shapes:** - Calculate the number of squares in the 10th shape. - Calculate the number of squares in the 25th shape. - Derive a formula to find the number of squares in the nth shape. **Calculation Tips:** - Observe the pattern: Each new shape adds 4 new squares, one on each arm. - Initial number of squares in the 1st figure is 5. - Notice the increment step-wise for each subsequent figure. **Additional Questions:** * 10th Shape: \( \text{Pattern: 4(n-1) + 5} \) squares * 25th Shape: \( \text{Pattern: 4(n-1) + 5} \) squares * nth Shape: \( \text{Pattern: 4(n-1) + 5} \) squares For more challenging math problems, visit our **Math Challenges** section!
Transcribed Image Text:**Title: Growing Pattern Problem** **Objective:** Comprehend the pattern and extend it to predict the number of squares in specified position. **Instructions:** 1. **Task:** Draw the next two shapes in the pattern provided. 2. **Pattern Recognition:** Study the given shapes and identify the pattern of growth. **Illustration:** - The figure showcases three shapes arranged in a sequential pattern: - The 1st shape has 5 squares forming a plus sign with a shaded square in the center. - The 2nd shape has 9 squares arranged in a larger plus sign with 1 square added to each arm of the previous plus sign. The center square remains shaded. - The 3rd shape has 13 squares forming an even larger plus sign with 1 additional square appended to each extended arm from the previous shape. The center square stays shaded. 3. **Extension Questions:** - **Determine the number of squares in future shapes:** - Calculate the number of squares in the 10th shape. - Calculate the number of squares in the 25th shape. - Derive a formula to find the number of squares in the nth shape. **Calculation Tips:** - Observe the pattern: Each new shape adds 4 new squares, one on each arm. - Initial number of squares in the 1st figure is 5. - Notice the increment step-wise for each subsequent figure. **Additional Questions:** * 10th Shape: \( \text{Pattern: 4(n-1) + 5} \) squares * 25th Shape: \( \text{Pattern: 4(n-1) + 5} \) squares * nth Shape: \( \text{Pattern: 4(n-1) + 5} \) squares For more challenging math problems, visit our **Math Challenges** section!
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