1. **Stating the problem:** We are given the series: A 7 9 H' 9 12 C 12 16 J ? and asked to find the next element. 2. **Analyzing the series:** The series alternates between letters and numbers. The letters are A, H', C, J, and the numbers are 7, 9, 9, 12, 12, 16. 3. **Looking at the letters:** The letters appear in the pattern A, H', C, J. Let's consider their positions in the alphabet: - A is the 1st letter - H is the 8th letter - C is the 3rd letter - J is the 10th letter 4. **Looking at the numbers:** The numbers appear in pairs: (7,9), (9,12), (12,16). Each pair increases: - 7 to 9 increases by 2 - 9 to 12 increases by 3 - 12 to 16 increases by 4 5. **Predicting the next number pair:** Following the pattern, the next increase should be by 5: $$16 + 5 = 21$$ 6. **Predicting the next letter:** The letters alternate between a pattern of positions: 1 (A), 8 (H), 3 (C), 10 (J). The pattern alternates between adding 7 and subtracting 5: - From A (1) to H (8): +7 - From H (8) to C (3): -5 - From C (3) to J (10): +7 Following this, the next letter should be: $$10 - 5 = 5$$ The 5th letter is E. 7. **Final answer:** The next element in the series is the letter E. **Answer:** E