Insert the missing term so that the differences are consecutive squares: 16, ?, 21, 30, 46, 71, 107.

Introduction / Context:We aim for differences that follow perfect squares in order, a frequent pattern in progressive series.

Given Data / Assumptions:

• Sequence: 16, ?, 21, 30, 46, 71, 107.
• Target differences: 1, 4, 9, 16, 25, 36 (i.e., 1^2 through 6^2).

Concept / Approach:Work from the known tail: 21→30 = 9, 30→46 = 16, 46→71 = 25, 71→107 = 36. So just before 21 the difference must be 4, and before that 1.

Step-by-Step Solution:

Verification / Alternative check:All differences match 1^2, 2^2, 3^2, 4^2, 5^2, 6^2 in order.

Why Other Options Are Wrong:19, 21, 23 would break the square-difference progression somewhere else.

Common Pitfalls:Assuming constant differences; here they grow as perfect squares.

Final Answer:17.