Letter Series Pattern Analysis

The given series consists of groups of consecutive letters: BC, FGH, LMNO.

Analyzing the Number of Letters

First, let's observe the length of each group in the series:

• BC has 2 letters.
• FGH has 3 letters.
• LMNO has 4 letters.

The number of letters in each group is increasing by 1. Therefore, the missing group should contain 5 letters.

Analyzing the Starting Letters

Next, let's examine the starting letter of each group and its position in the alphabet:

• B is the 2^nd letter.
• F is the 6^th letter.
• L is the 12^th letter.

Identifying the Pattern in Starting Letters

We look at the difference between the positions of the starting letters:

• Position difference between F and B: $6 - 2 = 4$.
• Position difference between L and F: $12 - 6 = 6$.

The differences are 4 and 6. This sequence of differences (4, 6) is increasing by 2. The next difference in this pattern should be $6 + 2 = 8$.

Determining the Missing Group

To find the starting letter of the missing group, we add the next difference (8) to the position of the last starting letter (L, which is 12):

• Position of the next starting letter: $12 + 8 = 20$.

The 20^th letter of the alphabet is T.

Since the missing group must have 5 letters (as determined earlier) and starts with T, the group is formed by the next 5 consecutive letters starting from T:

• T (20^th letter)
• U (21^st letter)
• V (22^nd letter)
• W (23^rd letter)
• X (24^th letter)

Thus, the missing group of letters is TUVWX.