A three letter series is given as BMY, DNW, FOU, ? Choose the correct alternative from the options that will complete this series using the pattern in the English alphabet.

Introduction / Context:
This is a three letter alphabet series. The given terms are BMY, DNW, FOU, followed by a missing term. Each term consists of three letters and there is usually a consistent pattern along each column of first, second, and third letters. The task is to decode this pattern and apply it to find the next three letter group.

Given Data / Assumptions:

• Series: BMY, DNW, FOU, ? • Options: GHO, HGO, HPS, HPT • Alphabet positions: B 2, C 3, D 4, E 5, F 6, G 7, H 8, M 13, N 14, O 15, P 16, Q 17, R 18, S 19, T 20, U 21, V 22, W 23, Y 25. • Assumption: Each column of letters follows a numeric pattern like constant difference or a steadily increasing step.

Concept / Approach:
We split the triplets into three sequences: one for first letters, one for second, and one for third. For each sequence we calculate positions and differences. The first letters appear to increase by a constant amount, the second letters show a simpler step pattern, and the third letters move with their own consistent difference. Once we determine these patterns, we extend each sequence by one term and then recombine the predicted letters to obtain the missing group.

Step-by-Step Solution:
Step 1: First letters: B, D, F. Positions are 2, 4, and 6, so they increase by +2 each time. Step 2: Extend first letter sequence: 6 + 2 = 8, which is H. So the next first letter is H. Step 3: Second letters: M, N, O. Positions are 13, 14, and 15, so they increase by +1 each time. Step 4: Extend second letter sequence: 15 + 1 = 16, which is P. So the next second letter is P. Step 5: Third letters: Y, W, U. Positions are 25, 23, and 21, so they decrease by 2 each time (25 to 23, 23 to 21). Step 6: Extend third letter sequence: 21 − 2 = 19, which is S. So the next third letter is S. Step 7: Combining all predicted letters gives H, P, and S, so the missing term is HPS.

Verification / Alternative check:
We can rewrite the sequence of triplets as numeric columns: first column (2,4,6,8), second column (13,14,15,16), third column (25,23,21,19). These clearly show a pattern of +2, +1, and −2 respectively. Turning the last set (8,16,19) back into letters yields H, P, S, which matches option HPS. No other option has exactly this combination of letters, and any other choice would break at least one of the column wise patterns.

Why Other Options Are Wrong:
GHO has first letter G, which would mean a jump of only +1 from F instead of the required +2, and its second and third letters also do not match the established progressions. HGO and HPT each violate the steady +1 increase in the second letter column or the −2 decrease in the third letter column when checked in detail.

Common Pitfalls:
A common mistake is to guess based on partial recognition such as noticing that the first letters go up by two and then picking any option that begins with H. Without checking the second and third letters, this often leads to errors. It is crucial to examine all columns systematically and to compute differences numerically rather than relying on approximate visual impressions.

Final Answer:
The three letter group that completes the series BMY, DNW, FOU is HPS.