Perfect squares of consecutive odd integers: 1, 9, 25, 49, 81, ? Find the next term.

Introduction / Context:
The given list looks like perfect squares: 1 = 1^2, 9 = 3^2, 25 = 5^2, 49 = 7^2, 81 = 9^2. Recognizing this establishes a crystal-clear continuation rule.

Given Data / Assumptions:

• Sequence: 1, 9, 25, 49, 81.
• Indices of odd integers: 1, 3, 5, 7, 9.

Concept / Approach:
The next odd integer after 9 is 11, so the next perfect square is 11^2. This is the simplest interpretation consistent with all provided terms.

Step-by-Step Solution:
Map terms to odd squares: 1^2, 3^2, 5^2, 7^2, 9^2.Next odd integer = 11.Next term = 11^2 = 121.

Verification / Alternative check:
No alternative simple pattern (e.g., constant differences) fits as cleanly: differences 8, 16, 24, 32 already reflect the (2n−1)-square structure.

Why Other Options Are Wrong:
90, 125, 135 are not perfect squares; selecting these would break the square-of-odd rule evident in the data.

Common Pitfalls:
Stopping at differences and missing the well-known odd-squares identity: the difference between consecutive odd squares increases by 8 each time.

Final Answer:
121