Compute the next value: 8, 28, 116, 584, ? — detect the repeated “multiply and then add a constant” rule to continue the sequence correctly.

Introduction / Context:This series is built by multiplying by an increasing integer and then adding a fixed constant. Recognizing that two-step pattern (multiply, then add) provides a direct path to the next term.

Given Data / Assumptions:

• Sequence: 8 → 28 → 116 → 584 → ?
• We suspect: multiply by n, then add a fixed small number.

Concept / Approach:Check consecutive ratios to see the approximate multiplier, then verify whether a small constant (e.g., +4) is added. Confirm across steps; if consistent, apply the next multiplier and the same addend.

Step-by-Step Solution:

Verification / Alternative check:No other simple constant addend fits all prior links. The increasing multipliers (3, 4, 5, 6) plus a constant +4 produce exact matches every time.

Why Other Options Are Wrong:

• 1752, 3502, 3504 do not result from the required “×6 then +4” step.

Common Pitfalls:Attempting to use only multiplication without checking for a small additive constant, which is a frequent twist in series puzzles.

Final Answer:3508