In the alphabet series ABC, BDF, DHL, which of the following three letter groups should come next to continue the same pattern?

Introduction / Context:
This series question looks more challenging than a typical alphabet progression. The terms are ABC, BDF, DHL and ?, and we must select the next three letter group from the options. At first glance, the groups do not appear to be simply consecutive letters. Instead, the pattern is hidden in how each column of letters (first, second and third positions) advances across the series. This type of problem tests a higher level of abstraction in sequence recognition, often involving changing step sizes rather than fixed increments.

Given Data / Assumptions:

• Known terms: ABC, BDF, DHL, ?.• First letters form the series: A, B, D, ?.• Second letters form: B, D, H, ?.• Third letters form: C, F, L, ?.• Alphabet positions: A=1, B=2, ..., Z=26.

Concept / Approach:
The key idea is to study how each column of letters changes from term to term. In many advanced alphabet questions, the differences between letters themselves follow arithmetic patterns. Here, each column has its own increasing difference. When we compute these differences carefully, we see that the increments in each column double at each step, creating a pattern that we can extrapolate to find the next term.

Step-by-Step Solution:
Step 1: Look at the first letters: A, B, D.Positions are A=1, B=2, D=4.Step 2: Differences: B − A = 1 and D − B = 2. The increments are 1 and then 2, suggesting that the next increment should be 4 (doubling each time: 1, 2, 4, 8).Step 3: The next first letter position is 4 + 4 = 8, which is H.Step 4: Now consider second letters: B, D, H.Positions: B=2, D=4, H=8.Step 5: Differences: 4 − 2 = 2, 8 − 4 = 4, again doubling. The next increment should be 8.Step 6: Next second letter position: 8 + 8 = 16, which corresponds to P.Step 7: Third letters: C, F, L.Positions: C=3, F=6, L=12.Step 8: Differences: 6 − 3 = 3 and 12 − 6 = 6, doubling once again. The next increment should be 12.Step 9: Next third letter position: 12 + 12 = 24, which is X.Step 10: Therefore, the next triplet in the series is HPX.

Verification / Alternative check:
If we summarise the pattern, the first column uses increments 1, 2, 4, 8, the second column uses 2, 4, 8 and the third column uses 3, 6, 12. This creates a consistent theme of doubling differences across columns. Substituting HPX back into the series gives ABC, BDF, DHL, HPX, which is compatible with all the identified rules. No other option aligns with this three dimensional structure across all columns.

Why Other Options Are Wrong:
RST and CDE look like simple sequences of consecutive letters but do not respect the specific numeric jumps in each column. For example, switching from third letters L to T in RST does not maintain a difference of 12. EGF also fails to continue the doubling pattern in any column. Only HPX has H as the first letter, P as the second and X as the third in a way that preserves the increasing increments of 1, 2, 4, 8 for first letters, 2, 4, 8, 16 for second letters and 3, 6, 12, 24 for third letters.

Common Pitfalls:
A common error is to assume that all three letters in each term must be consecutive or that the series must be a simple shift of ABC forward. This leads to favouring options like CDE or RST. Another pitfall is to examine only one column while ignoring the others, producing an incomplete pattern. In advanced alphabet series, each position often has its own rule, and all three rules must be satisfied simultaneously for an option to be correct.

Final Answer:
HPX