Step 1: Understanding the Concept:
This is a sequence of four-letter groups. To find the missing group, we must decipher both the pattern of letters within each group and the pattern that links one group to the next.
Step 2: Key Formula or Approach:
Convert the letters into their numerical positions in the alphabet to analyze the arithmetic patterns.
Step 3: Detailed Explanation:
1. Analyze the pattern between the groups:
Let's look at the first letter of each group: D, G, J.
- D = 4
- G = 7
- J = 10
The difference is \(7-4=3\) and \(10-7=3\). This is an arithmetic progression with a common difference of +3.
The first letter of the next group should be \(10+3=13\). The 13th letter is M.
2. Analyze the pattern within each group:
Let's examine the numerical differences between the letters in the first group, DFIK.
- D = 4
- F = 6
- I = 9
- K = 11
The differences are: \(6-4 = +2\), \(9-6 = +3\), \(11-9 = +2\). The pattern is (+2, +3, +2).
Let's verify this pattern in the other groups.
- GILN: G(7), I(9), L(12), N(14). Differences are \(+2, +3, +2\). The pattern holds.
- JLOQ: J(10), L(12), O(15), Q(17). Differences are \(+2, +3, +2\). The pattern holds.
3. Construct the missing group:
The missing group starts with M (13). We apply the internal pattern (+2, +3, +2).
- First letter: M (13)
- Second letter: 13 + 2 = 15. The 15th letter is O.
- Third letter: 15 + 3 = 18. The 18th letter is R.
- Fourth letter: 18 + 2 = 20. The 20th letter is T.
The missing group is MORT.
Step 4: Final Answer:
The missing letter group is MORT, which corresponds to option (C).