1. The problem is to find the next number in the sequence: 10, 15, 5, 25, 20, ... 2. Let's analyze the pattern by looking at the differences between consecutive terms: - From 10 to 15: increase by 5 - From 15 to 5: decrease by 10 - From 5 to 25: increase by 20 - From 25 to 20: decrease by 5 3. The pattern of changes seems to alternate between increase and decrease with varying amounts: +5, -10, +20, -5. 4. Let's check if the increases and decreases follow a pattern: - Increases: 5, 20 (multiplied by 4) - Decreases: 10, 5 (divided by 2) 5. The increases are multiplied by 4, then the decreases are divided by 2, but the pattern is not consistent. 6. Another approach is to look at the sequence in pairs: - (10, 15), (5, 25), (20, ?) 7. The first pair increases by 5, the second pair increases by 20, the third pair might increase by 5 again. 8. Alternatively, the sequence might be alternating between adding and subtracting numbers: +5, -10, +20, -5, so the next change might be -10. 9. Applying -10 to the last term 20 gives: $$20 - 10 = 10$$ 10. Therefore, the next number in the sequence is 10. Final answer: 10