Finding the Missing Term in the Letter Series

The question asks us to identify the missing term in the given series of four-letter words: XFCJ, ADFH, ?, GZLD, JXOB. To solve this, we need to analyze the pattern governing the sequence of letters.

Analyzing Letter Position Patterns

We can break down the series by looking at the pattern of change for each letter position (1st, 2nd, 3rd, and 4th) across the terms.

First, let's assign numerical values to each letter based on its position in the alphabet (A=1, B=2, ..., Z=26).

Pattern Analysis: 1st Letter

The sequence for the first letters is: X (24), A (1), ?, G (7), J (10).

• The change from G (7) to J (10) is an increase of 3 ($10 - 7 = 3$).
• Let's assume this '+3' pattern continues backward and forward.
• From A (1), adding 3 gives the 4th position: $1 + 3 = 4$.
• From the 4th position, adding 3 gives the 7th position: $4 + 3 = 7$ (which is G). This matches.
• Now let's check the start. From X (24), we need to get to A (1). If we add 3, we get $24 + 3 = 27$. Since there are only 26 letters, we wrap around: $27 \pmod{26} = 1$. This matches A (1).
• Therefore, the pattern for the first letter is adding 3 (with wrap-around). The missing letter is at the 4th position, which is D.

Pattern Analysis: 2nd Letter

The sequence for the second letters is: F (6), D (4), ?, Z (26), X (24).

• The change from X (24) to Z (26) is not straightforward by adding. Let's check subtraction. Moving backward: Z (26) to X (24) is a decrease of 2 ($24 - 26 = -2$).
• Let's assume this '-2' pattern continues forward and backward.
• From F (6), subtracting 2 gives the 4th position: $6 - 2 = 4$. This matches D (4).
• From D (4), subtracting 2 gives the 2nd position: $4 - 2 = 2$.
• From the 2nd position, subtracting 2 gives $2 - 2 = 0$. Wrapping around the alphabet (where 0 corresponds to 26), we get the 26th position: $0 \equiv 26 \pmod{26}$. This matches Z (26).
• The pattern holds. The missing letter is at the 2nd position, which is B.

Pattern Analysis: 3rd Letter

The sequence for the third letters is: C (3), F (6), ?, L (12), O (15).

• The change from C (3) to F (6) is an increase of 3 ($6 - 3 = 3$).
• The change from L (12) to O (15) is an increase of 3 ($15 - 12 = 3$).
• Assuming the '+3' pattern continues:
• From F (6), adding 3 gives the 9th position: $6 + 3 = 9$.
• From the 9th position, adding 3 gives the 12th position: $9 + 3 = 12$. This matches L (12).
• The pattern holds. The missing letter is at the 9th position, which is I.

Pattern Analysis: 4th Letter

The sequence for the fourth letters is: J (10), H (8), ?, D (4), B (2).

• The change from J (10) to H (8) is a decrease of 2 ($8 - 10 = -2$).
• The change from D (4) to B (2) is a decrease of 2 ($2 - 4 = -2$).
• Assuming the '-2' pattern continues:
• From H (8), subtracting 2 gives the 6th position: $8 - 2 = 6$.
• From the 6th position, subtracting 2 gives the 4th position: $6 - 2 = 4$. This matches D (4).
• The pattern holds. The missing letter is at the 6th position, which is F.

Constructing the Missing Term

By combining the deduced letters for each position, we get:

• 1st Letter: D
• 2nd Letter: B
• 3rd Letter: I
• 4th Letter: F

Putting these together forms the word DBIF.

Conclusion

The term that correctly replaces the question mark (?) in the series XFCJ, ADFH, ?, GZLD, JXOB is DBIF.