Number series (find the wrong term): 2, 6, 24, 96, 285, 568, 567

Introduction / Context:
Many series use repeated multiplication by small integers. Here the early terms suggest a clean multiplier pattern that one middle term violates. Identifying the intended rule lets us single out the erroneous value.

Given Data / Assumptions:

• Series: 2, 6, 24, 96, 285, 568, 567.
• Exactly one term is wrong.
• First three jumps look multiplicative.

Concept / Approach:
Check ratios between successive terms: 6/2=3, 24/6=4, 96/24=4. This indicates the multipliers 3, then 4, then 4 again. A natural continuation would be another simple integer multiplier next (e.g., *3 or *2). The most immediate consistency check is 96 * 3 = 288; compare with the given 285 to detect the likely misprint/error.

Step-by-Step Solution:
From 2 → 6 (×3), 6 → 24 (×4), 24 → 96 (×4).Continuing with a reasonable small-integer multiplier (×3), the next should be 96 × 3 = 288, but the series shows 285.Therefore 285 is the outlier; correcting it to 288 restores a smooth multiplicative pattern.Subsequent terms can then sensibly proceed (for example ×2 = 576, then −9 = 567 if a terminal tweak is intended), but the only clearly inconsistent value relative to the immediate prior step is 285.

Verification / Alternative check:
Local consistency check: all earlier steps are exact integer multipliers; only 96 → 285 fails that property (it is not a neat multiplication by any small integer). Replacing 285 with 288 fixes the break.

Why Other Options Are Wrong:

• 6, 24, 96, 567 each can be reconciled with reasonable subsequent steps once 285 is corrected; none is as clearly inconsistent as 285.

Common Pitfalls:

• Overfitting late terms; for error-spotting, prioritize the first clear violation of an emerging rule.

Final Answer:
285