What will be the next term in the following ? DCXW, FEVU, HGTS, ?

Concept: In an alphabet series each letter is first replaced by its position in the English alphabet (A = 1, B = 2, … , Z = 26). The pattern of the series is then the fixed arithmetic that carries the positions of one term to the positions of the next term, slot by slot. The missing term is obtained by applying that same arithmetic once more to the last given term, and only then converting the numbers back into letters.

Application. Decode the three given terms into alphabet positions:

Now read each slot down its own column and find its step:

1. Slot 1: 4 → 6 → 8. Each step adds 2.

2. Slot 2: 3 → 5 → 7. Each step adds 2.

3. Slot 3: 24 → 22 → 20. Each step subtracts 2.

4. Slot 4: 23 → 21 → 19. Each step subtracts 2.

5. Apply one more step to the last given term (8, 7, 20, 19): 8 + 2 = 10, 7 + 2 = 9, 20 − 2 = 18, 19 − 2 = 17.

6. Convert 10, 9, 18, 17 back into letters: 10 = J, 9 = I, 18 = R, 17 = Q.

7. The next term is therefore JIRQ.

Cross-check (second, independent route). Look at the internal build of each given term instead of the column steps. Its first two letters are consecutive and descending (D, C / F, E / H, G), its last two letters are also consecutive and descending (X, W / V, U / T, S), and every front letter pairs with a back letter to sum to 27: D + W = 4 + 23 = 27, C + X = 3 + 24 = 27, and the same holds in FEVU and HGTS. The fourth term must open two places after H, that is J = 10, followed by I = 9. Its back pair is then fixed at 27 − 9 = 18 = R and 27 − 10 = 17 = Q, which rebuilds JIRQ without using the column steps at all.

Contrast with the other groups offered.

• AKPO opens at A = 1 instead of J = 10, so its first slot ignores the +2 column step, and its interior jump K → P (+5) matches nothing in the given terms.

• ABYZ climbs inside both of its pairs (1, 2 and 25, 26), while every given term descends inside both of its pairs.

• LMRS opens at L = 12, which is four places past H rather than two, and it also climbs inside both pairs (12, 13 and 18, 19).