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, ? The numbers appear in pairs: (7,9), (9,12), (12,16), and then a missing number after J. 3. **Looking at the numbers:** - From 7 to 9, increase by 2. - From 9 to 12, increase by 3. - From 12 to 16, increase by 4. The increments are increasing by 1 each time. 4. **Predicting the next number:** - The next increment should be 5. - So, after 16, the next number is $$16 + 5 = 21$$. 5. **Looking at the letters:** - Letters are A, H', C, J, ? - Let's look at their positions in the alphabet: - A = 1 - H = 8 - C = 3 - J = 10 6. **Finding a pattern in letters:** - From A (1) to H (8): +7 - From H (8) to C (3): -5 - From C (3) to J (10): +7 The pattern alternates +7, -5, +7, so the next should be -5 from J (10): $$10 - 5 = 5$$ which corresponds to E. 7. **Conclusion:** The next letter is E and the next number is 21. 8. **Checking the options:** The options given are A 12, B 16, C 17, D D, E E. The best answer is E (letter E), matching our letter prediction. **Final answer:** E