Challenge: 2, 6, 12, 20, __

Pattern: The pattern in this sequence is that each number is increasing by adding consecutive odd numbers.

Explanation: - 2 + 4 (2nd odd number) = 6 - 6 + 6 (3rd odd number) = 12 - 12 + 8 (4th odd number) = 20

Therefore, the next number in the sequence would be 20 + 10 (5th odd number) = 30.

Strategies for recognizing and extending patterns: 1. Look for relationships between consecutive numbers in the sequence. 2. Identify any common operations or patterns that are being applied to each number. 3. Try different strategies such as adding, subtracting, multiplying, or dividing to find the pattern. 4. Use trial and error to test different hypotheses and see if they fit the sequence. 5. Once a pattern is identified, use it to extend the sequence and find the next number.