Find the next term of the letter series. AaC, BbD, DdF, HhJ, _____

Concept

In an alphabet series every letter is first replaced by its position in the English alphabet (A = 1, B = 2, ... Z = 26). Each slot of a term then carries its own independent rule: a slot may advance by a constant difference, may grow geometrically so that each value is a fixed multiple of the previous one, or may simply mirror another slot of the same term.

The next term is built by applying every slot rule exactly once more, so all three slots must be resolved separately before a term can be chosen.

Application

1. Write the leading capitals as alphabet positions: A = 1, B = 2, D = 4, H = 8.

2. Each leading position is twice the one before it: 1 x 2 = 2, 2 x 2 = 4, 4 x 2 = 8. Applying the same doubling once more gives 8 x 2 = 16, and the 16th letter of the alphabet is P.

3. Compare the closing letter of each term with its own leading letter: C(3) - A(1) = 2, D(4) - B(2) = 2, F(6) - D(4) = 2, J(10) - H(8) = 2. The closing slot always sits two places after the leading slot, so it is 16 + 2 = 18, the letter R.

4. The lowercase middle slot repeats the term's own leading capital in small case (A gives a, B gives b, D gives d, H gives h), so with P leading the middle letter is p.

5. Combining the three slots, the next term of the series is PpR.

Cross-check

Reading the leading and closing positions of each offered term against the required 16 and 18 settles the choice:

Only 16 continues the doubling 1, 2, 4, 8, and only that leading position places the closing slot on 18. The next term of the series is therefore PpR.