Number series – add descending perfect squares (14^2, 13^2, 12^2, 11^2, 10^2): 4, 200, 369, 513, 634, ?

Introduction / Context:Another classic pattern is adding consecutive perfect squares (often descending). Once identified, extension is immediate and exact.

Given Data / Assumptions:

• 4→200 (+196 = 14^2)
• 200→369 (+169 = 13^2)
• 369→513 (+144 = 12^2)
• 513→634 (+121 = 11^2)

Concept / Approach:Continue with the next lower square: 10^2 = 100.

Step-by-Step Solution:

Verification / Alternative check:All increments are perfect squares descending by 1 in the base (14, 13, 12, 11, 10).

Why Other Options Are Wrong:

Common Pitfalls:Attempting ratios between terms; the additive square structure fits perfectly.

Final Answer:734