Number series – find the next term. Sequence: 1, 4, 9, 16, 25, 36, 49, ( ? )

Introduction / Context:This sequence is the classic list of perfect squares in ascending order. Recognizing square numbers is a foundational skill in quantitative reasoning questions.

Given Data / Assumptions:

• Given terms: 1, 4, 9, 16, 25, 36, 49
• These are 1^2 through 7^2.

Concept / Approach:Perfect squares follow n^2 for integer n. The next integer after 7 is 8, therefore the next square is 8^2.

Step-by-Step Solution:

Verification / Alternative check:Confirm earlier values: 6^2 = 36 and 7^2 = 49. The progression is consistent, so 8^2 is the next logical term.

Why Other Options Are Wrong:

• 54 and 56: Not perfect squares.
• 81: That is 9^2, which would be the term after 64, not immediately next to 49 if stepping by single integers.

Common Pitfalls:Confusing square numbers with triangular or other figurate numbers. Always check n^2 explicitly.

Final Answer:64