Number series — subtract consecutive perfect squares: Complete the series: 41, 40, 36, ?, 11

Introduction / Context:Some decreasing sequences are generated by subtracting perfect squares in order. Recognizing the first few subtractions often reveals the pattern immediately.

Given Data / Assumptions:

• Series: 41, 40, 36, ?, 11
• Observe differences: −1, −4, −9, −16 are 1^2, 2^2, 3^2, 4^2 in order.

Concept / Approach:Subtract successive square numbers starting at 1^2. Insert the missing value that keeps the pattern consistent.

Step-by-Step Solution:41 − 1^2 = 4040 − 2^2 = 3636 − 3^2 = 27 ← missing term27 − 4^2 = 11

Verification / Alternative check:The complete sequence becomes 41, 40, 36, 27, 11 with consecutive subtractions of 1, 4, 9, 16.

Why Other Options Are Wrong:30, 29, or 35 would break the exact squares subtraction cadence.

Common Pitfalls:Mixing up additive and subtractive square patterns; always check a few steps forward.

Final Answer:27