Step 1: Understanding the Concept:
This is a sequence of letter groups. To solve it, we need to identify two patterns: the pattern of letters within each group, and the pattern that connects one group to the next.
Step 2: Key Formula or Approach:
We will convert the letters to their numerical positions in the alphabet to analyze the patterns more easily.
Step 3: Detailed Explanation:
1. Analyze the pattern within each group:
Let's look at the numerical positions of the letters in the given groups.
- ABD: A(1), B(2), D(4). The difference between letters is \(+1, +2\).
- EFH: E(5), F(6), H(8). The difference between letters is \(+1, +2\).
- MNP: M(13), N(14), P(16). The difference between letters is \(+1, +2\).
- QRT: Q(17), R(18), T(20). The difference between letters is \(+1, +2\).
The internal pattern for each group is consistent: the second letter is one position after the first, and the third letter is two positions after the second.
2. Analyze the pattern between the groups:
Let's look at the sequence of the first letters of each group: A, E, __, M, Q.
Their numerical positions are:
- A = 1
- E = 5
- __ = ?
- M = 13
- Q = 17
Let's find the difference between these positions:
- From A(1) to E(5) is a jump of \(+4\).
- From M(13) to Q(17) is a jump of \(+4\).
This suggests a constant jump of +4 between the first letters of consecutive groups.
Let's apply this to find the missing first letter:
The first letter of the missing group should be E(5) + 4 = 9. The 9th letter is I.
Let's check if this is consistent with the rest of the sequence: I(9) + 4 = 13, which is M. Correct.
So, the missing group must start with the letter I.
3. Construct the missing group:
The missing group starts with I. We apply the internal pattern we found in part 1 (\(+1, +2\)).
- First letter: I (9)
- Second letter: 9 + 1 = 10, which is J.
- Third letter: 10 + 2 = 12, which is L.
The missing group is IJL.
Step 4: Final Answer:
The missing letter group is IJL, which corresponds to option (C).