Understanding the Alphabetical Series Pattern

The question asks us to identify the next term in the given alphabetical series: GTY ANS UHM OBG ?. We need to find the pattern governing the sequence of these three-letter groups.

Analyzing the Series Terms

Let's represent each letter by its position in the English alphabet (A=1, B=2, ..., Z=26).

Identifying the Pattern Rule

We examine the difference between the positions of corresponding letters in consecutive terms. Let's look at the shift for each position:

Pattern for the 1st Letter:

• G (7) to A (1): The difference is $1 - 7 = -6$.
• A (1) to U (21): Using modular arithmetic (wrapping around the alphabet), $1 - 6 \equiv -5 \pmod{26}$. The $21^{st}$ letter is U. This is equivalent to shifting back 6 positions: A $\rightarrow$ Z $\rightarrow$ Y $\rightarrow$ X $\rightarrow$ W $\rightarrow$ V $\rightarrow$ U.
• U (21) to O (15): The difference is $15 - 21 = -6$.
• O (15) to I (9): The difference is $9 - 15 = -6$.

The pattern for the first letter is a consistent decrease of 6 positions.

Pattern for the 2nd Letter:

• T (20) to N (14): The difference is $14 - 20 = -6$.
• N (14) to H (8): The difference is $8 - 14 = -6$.
• H (8) to B (2): The difference is $2 - 8 = -6$.
• B (2) to V (22): Using modular arithmetic, $2 - 6 \equiv -4 \pmod{26}$. The $22^{nd}$ letter is V. This is equivalent to shifting back 6 positions: B $\rightarrow$ A $\rightarrow$ Z $\rightarrow$ Y $\rightarrow$ X $\rightarrow$ W $\rightarrow$ V.

The pattern for the second letter is also a consistent decrease of 6 positions.

Pattern for the 3rd Letter:

• Y (25) to S (19): The difference is $19 - 25 = -6$.
• S (19) to M (13): The difference is $13 - 19 = -6$.
• M (13) to G (7): The difference is $7 - 13 = -6$.
• G (7) to A (1): The difference is $1 - 7 = -6$.

The pattern for the third letter is also a consistent decrease of 6 positions.

Applying the Pattern to Find the Missing Term

Since each letter in the series decreases by 6 positions (modulo 26), we apply this rule to the last known term, OBG:

• 1st Letter: O is the 15^th letter. Applying the rule: $15 - 6 = 9$. The 9^th letter is I.
• 2nd Letter: B is the 2^nd letter. Applying the rule: $2 - 6 = -4$. Wrapping around the alphabet, $-4$ corresponds to the $(26 - 4) = 22^{nd}$ position. The 22^nd letter is V.
• 3rd Letter: G is the 7^th letter. Applying the rule: $7 - 6 = 1$. The 1^st letter is A.

Combining these results, the missing term is IVA.

Conclusion

The term that should come in place of the question mark (?) in the series GTY ANS UHM OBG ? is IVA.

This corresponds to Option 4.