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The image contains a series of mathematical exercises in Arabic, focusing on identifying patterns in sequences and completing them. Below is a breakdown and solution for each sequence:

1. **Sequence 14: \(0, 2, 4, 6, 8, \dots\)**
   - This is an arithmetic sequence where each term increases by 2. 
   - The next term is \(8 + 2 = 10\).

2. **Sequence 15: \(3, 6, 9, 12, 15, \dots\)**
   - This sequence increases by 3 each time.
   - The next term is \(15 + 3 = 18\).

3. **Sequence 16: \(4, 8, 12, 16, 20, \dots\)**
   - Each term increases by 4.
   - The next term is \(20 + 4 = 24\).

4. **Sequence 17: \(2, 22, 222, 2222, \dots\)**
   - The pattern is formed by adding an extra "2" to the number.
   - The next term is \(22222\).

5. **Sequence 18: \(1, 4, 9, 16, \dots\)**
   - These are squares of natural numbers: \(1^2, 2^2, 3^2, 4^2\).
   - The next term is \(5^2 = 25\).

6. **Sequence 19: \(1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \dots\)**
   - This is a geometric sequence where each term is multiplied by \(\frac{1}{2}\).
   - The next term is \(\frac{1}{16}\).

Would you like further explanations or details on any specific sequence? 

### Related Questions:
1. What are the general formulas for arithmetic and geometric sequences?
2. How can you identify if a sequence is arithmetic or geometric?
3. What are some real-world applications of arithmetic sequences?
4. How do you find the sum of the first \(n\) terms of a geometric sequence?
5. What is the difference between finite and infinite sequences?

**Tip:** Always look for a common difference or ratio when identifying patterns in sequences.

Write the general rule for each sequence and use it to find the next term in each sequence: 0, 2, 4, 6, 8,...; 3, 6, 9, 12, 15,...; 4, 8, 12, 16, 20,...; 2, 22, 222, 2222,...; 1, 4, 9, 16,...; 1, 1/2, 1/4, 1/8,...

Learn how to find the next term in arithmetic and geometric sequences, such as 0, 2, 4, 6, 8,... and 1, 1/2, 1/4, 1/8,... Discover the rules for these patterns and master the use of formulas for sequence calculations. Suitable for students in Grades 5-8.

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