Step 1: Understanding the Concept:
We have a sequence of three-letter groups. To find the missing group, we should analyze the pattern for each position (1st letter, 2nd letter, 3rd letter) across the sequence.
Step 2: Key Formula or Approach:
Convert all letters to their numerical positions in the alphabet (A=1, B=2, ...) and look for an arithmetic progression for each of the three letter positions.
Step 3: Detailed Explanation:
Let's write down the sequence and the positions of the letters:
- BAT: B(2), A(1), T(20)
- EDW: E(5), D(4), W(23)
- IHA: I(9), H(8), A(1 or 27) (We can treat the alphabet as cyclic, A=1=27)
1. Pattern for the First Letter:
The sequence is B, E, I, ___.
The positions are 2, 5, 9, ___.
The differences are: \(5-2 = +3\), \(9-5 = +4\).
The differences are increasing by 1. The next difference should be \(+5\).
The position of the next letter is \(9+5 = 14\). The 14th letter is N.
2. Pattern for the Second Letter:
The sequence is A, D, H, ___.
The positions are 1, 4, 8, ___.
The differences are: \(4-1 = +3\), \(8-4 = +4\).
The differences are increasing by 1. The next difference should be \(+5\).
The position of the next letter is \(8+5 = 13\). The 13th letter is M.
3. Pattern for the Third Letter:
The sequence is T, W, A, ___.
The positions are 20, 23, 1, ___.
The differences are: \(23-20 = +3\).
From W(23) to A(1), we can think of cycling through the alphabet. The jump is \(23 \to 24(X) \to 25(Y) \to 26(Z) \to 1(A)\), which is a jump of +4.
The differences are +3, +4. The next difference should be \(+5\).
The position of the next letter is \(1+5 = 6\). The 6th letter is F.
Constructing the missing group:
- 1st letter: N
- 2nd letter: M
- 3rd letter: F
The missing group is NMF.
Step 4: Final Answer:
The missing group in the sequence is NMF, which corresponds to option (D).