Number series – squares of increasing primes (next prime’s square): 529, 841, 961, 1369, 1681, 1849, ? Treat each term as p^2 for p prime and extend with the next prime available in the options.

Introduction / Context:The given numbers are perfect squares that align with successive primes: 23^2=529, 29^2=841, 31^2=961, 37^2=1369, 41^2=1681, 43^2=1849. The natural continuation would be 47^2=2209, followed by 53^2=2809, etc. Since 2209 is not among the options provided, we select the next prime square that is present.

Given Data / Assumptions:

• Primes used so far: 23, 29, 31, 37, 41, 43.
• Options include 2809 (53^2) and 3481 (59^2), but not 2209 (47^2).

Concept / Approach:Under the Recovery-First policy, preserve the “prime squares” rule and pick the next available prime’s square from the choices.

Step-by-Step Solution:

Verification / Alternative check:All listed terms are squares of primes; 2809 maintains that property and minimal forward jump given the choices.

Why Other Options Are Wrong:

Common Pitfalls:Insisting on 47^2; when the exact continuation is absent from choices, select the nearest valid continuation consistent with the rule.

Final Answer:2809