Alphabetical Series Pattern Analysis

The question presents a series of three-letter combinations: BIG, DKI, FMK, HOM, followed by a question mark (?). We need to identify the pattern governing this series to determine the missing element.

Let's break down the series by analyzing the position of each letter within the English alphabet and the pattern between consecutive terms.

Analyzing Letter Position Patterns

We can analyze the pattern by looking at the first, second, and third letters separately.

First Letter Pattern

• The first letters of the terms are B, D, F, H.
• Converting these letters to their respective positions in the alphabet: B is $2^{nd}$, D is $4^{th}$, F is $6^{th}$, H is $8^{th}$.
• The sequence of positions is $2, 4, 6, 8$.
• The pattern observed is an increment of $2$ for each subsequent term ($4-2=2$, $6-4=2$, $8-6=2$).
• Following this pattern, the next position should be $8 + 2 = 10$.
• The $10^{th}$ letter in the alphabet is J.

Second Letter Pattern

• The second letters of the terms are I, K, M, O.
• Converting these letters to their respective positions: I is $9^{th}$, K is $11^{th}$, M is $13^{th}$, O is $15^{th}$.
• The sequence of positions is $9, 11, 13, 15$.
• The pattern observed is an increment of $2$ for each subsequent term ($11-9=2$, $13-11=2$, $15-13=2$).
• Following this pattern, the next position should be $15 + 2 = 17$.
• The $17^{th}$ letter in the alphabet is Q.

Third Letter Pattern

• The third letters of the terms are G, I, K, M.
• Converting these letters to their respective positions: G is $7^{th}$, I is $9^{th}$, K is $11^{th}$, M is $13^{th}$.
• The sequence of positions is $7, 9, 11, 13$.
• The pattern observed is an increment of $2$ for each subsequent term ($9-7=2$, $11-9=2$, $13-11=2$).
• Following this pattern, the next position should be $13 + 2 = 15$.
• The $15^{th}$ letter in the alphabet is O.

Determining the Missing Term

Combining the results from the analysis of each letter's position:

• The next first letter is J.
• The next second letter is Q.
• The next third letter is O.

Therefore, the missing term in the series is JQO.