Q. What comes at X and Y respectively in the following sequence?

Explanation : 

1. Assign each month its number in the calendar year:
January = 1, February = 2, …, December = 12.

2. Observe that to move from term n to term n + 1 we subtract an increasing offset k (starting with k = 0) from the current month number, taking results modulo 12 (with 0 mapped to 12).

3. Verify the pattern:
• Term 1 → Term 2 (k = 0): 1 − 0 = 1 ⇒ January
• Term 2 → Term 3 (k = 1): 1 − 1 = 0 ⇒ 12 ⇒ December
• Term 3 → Term 4 (k = 2): 12 − 2 = 10 ⇒ October
• Term 4 → Term 5 (k = 3): 10 − 3 = 7 ⇒ July → X
• Term 5 → Term 6 (k = 4): 7 − 4 = 3 ⇒ March
• Term 6 → Term 7 (k = 5): 3 − 5 = −2 ⇒ +12 → 10 ⇒ October
• Term 7 → Term 8 (k = 6): 10 − 6 = 4 ⇒ April → Y
• Term 8 → Term 9 (k = 7): 4 − 7 = −3 ⇒ +12 → 9 ⇒ September

4. Conclusion: X = July, Y = April.