### Mathematical Patterns and SequencesThis section will help you understand how to identify and work with patterns in sequences of numbers. The exercises provided will involve circle formations and stacked cubes to help demonstrate these concepts.#### Circle Formation Questions1. **What is the total number of circles in picture 5? Explain your answer.**2. **How many circles are needed to form triangle picture 7? Give a reason for your answer.**3. **How many circles are needed to form triangle picture 8? Give a reason for your answer.**4. **Complete the table below. Show all your calculations:**| Picture number | 1 | 2 | 3 | 4 | 5 | 6 | 12 | 15 ||--------------------|---|---|---|---|----|----|----|----|| Number of circles | 1 | 3 | 6 | 10 | 15 | 16 | 20 | 23 |*(16 marks)*#### Cube Stacking QuestionsStudy the diagrams and answer the following questions:- **Diagram Explanation:** - **Stack 1** shows a single cube. - **Stack 2** shows a stack of 8 cubes arranged in a 2x2x2 format. - **Stack 3** shows a stack of 27 cubes arranged in a 3x3x3 format.**Questions:**1. **How many cubes will there be in stack 5?**2. **Complete the table:**| Stack number | 1 | 2 | 3 | 4 | 5 | 6 | 10 ||-------------------|---|---|---|---|----|----|----|| Number of cubes | 1 | 8 | 27| | 125| 216| |3. **Write down the rule to calculate the number of cubes for any stack number:***(7 marks)*---**Total: (30 marks)****Note:** When solving these problems, look for patterns in the numbers and identify the rules that govern how these patterns are formed. The exercises are meant to enhance your ability to recognize and formulate numerical sequences.

To study the given figure and answer the given questions

Study the figure below and answer the following questions: Stack 1 Stack 2 Stack 3 i) How many cubes will there be in stack 5? ii) Complete the table. Stack 1 4. 6. 10 number Number 1 27 of cubes iii) Write down the rule to calculate the number of cubes for any stack number (7 marks) Total: (30 marks)

Study the figure below and answer the following questions: Stack 1 Stack 2 Stack 3 i) How many cubes will there be in stack 5? ii) Complete the table. Stack 1 4. 6. 10 number Number 1 27 of cubes iii) Write down the rule to calculate the number of cubes for any stack number (7 marks) Total: (30 marks)

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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Question

### Mathematical Patterns and Sequences

This section will help you understand how to identify and work with patterns in sequences of numbers. The exercises provided will involve circle formations and stacked cubes to help demonstrate these concepts.

#### Circle Formation Questions
1. **What is the total number of circles in picture 5? Explain your answer.**
2. **How many circles are needed to form triangle picture 7? Give a reason for your answer.**
3. **How many circles are needed to form triangle picture 8? Give a reason for your answer.**
4. **Complete the table below. Show all your calculations:**

| Picture number | 1 | 2 | 3 | 4 | 5 | 6 | 12 | 15 |
|--------------------|---|---|---|---|----|----|----|----|
| Number of circles | 1 | 3 | 6 | 10 | 15 | 16 | 20 | 23 |

*(16 marks)*

#### Cube Stacking Questions
Study the diagrams and answer the following questions:

- **Diagram Explanation:**
- **Stack 1** shows a single cube.
- **Stack 2** shows a stack of 8 cubes arranged in a 2x2x2 format.
- **Stack 3** shows a stack of 27 cubes arranged in a 3x3x3 format.

**Questions:**
1. **How many cubes will there be in stack 5?**
2. **Complete the table:**

| Stack number | 1 | 2 | 3 | 4 | 5 | 6 | 10 |
|-------------------|---|---|---|---|----|----|----|
| Number of cubes | 1 | 8 | 27| | 125| 216| |

3. **Write down the rule to calculate the number of cubes for any stack number:**

*(7 marks)*

---
**Total: (30 marks)**

**Note:** When solving these problems, look for patterns in the numbers and identify the rules that govern how these patterns are formed. The exercises are meant to enhance your ability to recognize and formulate numerical sequences.

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