1. The problem is to find the next number in the sequence: 13, 17, 71, 71, 17, 21, 25, ? 2. Let's analyze the sequence step-by-step: 3. The sequence is: 13, 17, 71, 71, 17, 21, 25, ? 4. Check for any obvious patterns such as differences between terms: Differences: 17 - 13 = 4 71 - 17 = 54 71 - 71 = 0 17 - 71 = -54 21 - 17 = 4 25 - 21 = 4 5. The differences are: 4, 54, 0, -54, 4, 4 6. Notice the pattern 4, 54, 0, -54, then 4, 4. The large jumps of 54 and -54 suggest a symmetry or repetition. 7. Also, the number 71 appears twice consecutively, and 17 appears twice but separated. 8. The last three differences are 4, 4, so if the pattern continues, the next difference might be 4 again. 9. Therefore, the next number is likely: $$25 + 4 = 29$$ 10. So, the next number in the sequence is 29.