A three letter series is given as BCF, CFI, DHL, ? Choose the correct alternative from the options that will complete this series based on the pattern in the English alphabet.

Introduction / Context:
This is a three letter alphabet series with the terms BCF, CFI, DHL, followed by a missing term. Each group contains three letters in a specific arrangement that involves different step sizes for the first, second, and third letters. The task is to decode this systematic pattern and extend it logically to find the next group from the given options.

Given Data / Assumptions:

• Series: BCF, CFI, DHL, ? • Options: EJO, CJM, EML, EMI • Alphabet positions: B 2, C 3, D 4, E 5, F 6, H 8, I 9, J 10, K 11, L 12, M 13, N 14, O 15. • Assumption: Each position (first, second, third letter) follows its own consistent numeric pattern across the terms.

Concept / Approach:
We examine each column of letters separately. The first letters B, C, D suggest a simple pattern, the second letters C, F, H reveal another, and the third letters F, I, L show yet another. By converting these letters into their numeric positions and analysing differences, we can extend each sequence. The correct next group must be the combination of the individually extended first, second, and third letter sequences.

Step-by-Step Solution:
Step 1: First letters: B, C, D have positions 2, 3, and 4. Step 2: The first letters increase by +1 each time (2 to 3, 3 to 4), so the next first letter should be 4 + 1 = 5, which is E. Step 3: Second letters: C, F, H have positions 3, 6, and 8. Step 4: Differences for second letters are +3 (3 to 6) and +2 (6 to 8). We can interpret this as a pattern where a smaller step follows a larger one. The most natural continuation is to repeat the earlier larger step of +2 after +3 and +2, giving a rising sequence of 3, 2, 2 for small alphabet ranges, though an even clearer clue comes from the third letter pattern. Step 5: Third letters: F, I, L have positions 6, 9, and 12. Step 6: Here the pattern is clean: the positions increase by +3 each time (6 to 9, 9 to 12). Step 7: Therefore, the next third letter should be at position 12 + 3 = 15, which is O. Step 8: We now look at the options and see that only EJO has third letter O. That fixes the third position. Step 9: Check second letter J of EJO: J is position 10. From H at position 8, a jump of +2 leads to 10, which fits the idea that the second letter sequence uses modest forward steps after going from C to F to H. Step 10: Putting all findings together, EJO maintains a smooth progression for first, second, and third letters and therefore is the correct continuation.

Verification / Alternative check:
We can summarise the column wise sequences as follows: first column B, C, D, E (2,3,4,5), second column C, F, H, J (3,6,8,10), third column F, I, L, O (6,9,12,15). Each sequence moves forward in a clear numeric pattern. The first column is +1 each step, the second column alternates between larger and smaller steps but remains strictly increasing, and the third column is +3 each step. EJO matches exactly these column values, whereas no other option yields 5 as first letter position and 15 as third letter position simultaneously.

Why Other Options Are Wrong:
CJM starts with C at position 3 rather than E at position 5 and breaks the straightforward +1 progression of the first letter sequence. EML and EMI both have third letters L and I, which correspond to positions 12 and 9, not 15, and therefore disrupt the +3 pattern in the third letter column.

Common Pitfalls:
Students may focus only on one column, such as the first or third, and then pick an option that matches partially, ignoring inconsistencies in the second letter. Another typical error is to overlook the smooth +3 pattern in the third column and instead try forcing an arithmetic sequence only in the second column. Checking all three columns together is crucial for choosing the unique option that fits all numeric progressions.

Final Answer:
The three letter group that correctly completes the series BCF, CFI, DHL is EJO.