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### Test 1: Identifying the Patterns
For each of the sequences given, the goal is to describe the rule that generates the sequence.

1. **12, 15, 18, 21, 24, 27, 30, 33**  
   Rule: This is an arithmetic sequence where the difference between consecutive terms is **+3**.

2. **45, 40, 35, 30, 25, 20, 15, 10**  
   Rule: This is an arithmetic sequence with a common difference of **-5**.

3. **6, 8, 10, 12, 14, 16, 18, 20**  
   Rule: This is another arithmetic sequence, with a common difference of **+2**.

4. **20, 30, 40, 50, 60, 70, 80**  
   Rule: This sequence increases by **+10** for each term, making it arithmetic.

5. **52, 49, 42, 35, 28, 21, 14, 7**  
   Rule: This sequence decreases by **-7**, which is also arithmetic.

### Test 2: Finding the Angles of Rotation
You are asked to find the angle of rotation for the following shapes:

1. **Square**  
   Rule: A square has 4 sides. The angle of rotation for regular polygons is given by:  
   \[
   \frac{360^\circ}{\text{number of sides}}
   \]
   Therefore, the angle of rotation for a square is:  
   \[
   \frac{360^\circ}{4} = 90^\circ
   \]

2. **Hexagon**  
   A hexagon has 6 sides, so its angle of rotation is:  
   \[
   \frac{360^\circ}{6} = 60^\circ
   \]

3. **Triangle**  
   A triangle (equilateral) has 3 sides, so its angle of rotation is:  
   \[
   \frac{360^\circ}{3} = 120^\circ
   \]

Let me know if you'd like further details or clarifications on any part.

### Related Questions:
1. What is a geometric sequence, and how does it differ from an arithmetic sequence?
2. Can the angle of rotation formula apply to irregular shapes?
3. What is the sum of the interior angles of a hexagon?
4. What are the rotational symmetries of a square?
5. How can you find a general formula for any polygon's angle of rotation?

### Tip: 
When solving patterns, always check whether the difference or ratio between terms is constant to determine whether the sequence is arithmetic or geometric.

Solve the sequences and find the angles of rotation for the given shapes.

This page explains how to solve arithmetic sequences and find the angles of rotation for shapes such as squares, hexagons, and triangles. It covers key concepts in geometry and arithmetic, suitable for students in Grades 4-6.

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