Series with square-step increments of 5k: Complete the series: 62, 87, 187, 412, 812, ?

Introduction / Context:
The jumps between terms are perfect squares of multiples of 5. Recognizing this gives a straightforward continuation.

Given Data / Assumptions:

• Series: 62, 87, 187, 412, 812, ?
• Differences: +25, +100, +225, +400 = 5^2, 10^2, 15^2, 20^2

Concept / Approach:
The next increment should be 25^2 = 625.

Step-by-Step Solution:
812 + 625 = 1437

Verification / Alternative check:
Initial term plus cumulative sums of (5k)^2 produces the listed numbers; adding (25)^2 fits the pattern.

Why Other Options Are Wrong:
1012, 1337, 1457 correspond to adding 200, 525, or 645, none of which are the required next square-of-5 multiple.

Common Pitfalls:
Assuming constant or linear growing differences; the key is the squared multiples.

Final Answer:
1437