https://file.aiquickdraw.com/mathbot/file/1725924918813wb375a87.jpg

Let's break down the image and help you solve the problems:

### Test 1: Sequence Rules
For each sequence, we need to identify the pattern and describe the rule.

1. **Sequence 1: 12, 15, 18, 21, 24, 27, 30, 33**
   - **Rule**: This is an arithmetic sequence where the common difference is +3. Each number is obtained by adding 3 to the previous one.

2. **Sequence 2: 45, 40, 35, 30, 25, 20, 15, 10**
   - **Rule**: This is an arithmetic sequence where the common difference is -5. Each number is obtained by subtracting 5 from the previous one.

3. **Sequence 3: 6, 8, 10, 12, 14, 16, 18, 20**
   - **Rule**: This is an arithmetic sequence where the common difference is +2. Each number is obtained by adding 2 to the previous one.

4. **Sequence 4: 20, 30, 40, 50, 60, 70, 80, 90**
   - **Rule**: This is an arithmetic sequence where the common difference is +10. Each number is obtained by adding 10 to the previous one.

5. **Sequence 5: 52, 49, 42, 35, 28, 21, 14, 7**
   - **Rule**: This is an arithmetic sequence where the common difference is -7. Each number is obtained by subtracting 7 from the previous one.

### Test 2: Angle of Rotation of Shapes

1. **Square**
   - A square has 4 sides, and its rotational symmetry occurs every \( \frac{360^\circ}{4} = 90^\circ \).
   - **Answer**: The angle of rotation for a square is **90 degrees**.

2. **Hexagon**
   - A regular hexagon has 6 sides, and its rotational symmetry occurs every \( \frac{360^\circ}{6} = 60^\circ \).
   - **Answer**: The angle of rotation for a hexagon is **60 degrees**.

3. **Triangle (Equilateral Triangle)**
   - An equilateral triangle has 3 sides, and its rotational symmetry occurs every \( \frac{360^\circ}{3} = 120^\circ \).
   - **Answer**: The angle of rotation for an equilateral triangle is **120 degrees**.

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Let me know if you'd like further details or if you have any questions! 

Here are 5 follow-up questions for further practice:

1. What would be the next three numbers in Sequence 2 if the pattern continued?
2. How do you calculate the angle of rotation for an octagon?
3. If the difference in a sequence changes every step, how would you describe that pattern?
4. Can the angle of rotation ever be greater than 360 degrees? Why or why not?
5. What would be the common difference in a sequence where the first term is 7 and the second term is 14?

**Tip**: In sequences, look for patterns like addition, subtraction, multiplication, or division to identify the rule.

Assessment in GE 4. Test 1: Describe the rule of each sequence. Test 2: Solve the angle of rotation for shapes (square, hexagon, triangle).

Solve arithmetic sequence rules and calculate rotational symmetry for common shapes like squares, hexagons, and triangles. This assessment covers core mathematical concepts suitable for grades 6-8.

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