Alternate ×3 and ÷2 pattern Complete the series: 8, 24, 12, 36, 18, 54, ( ... ).

Introduction / Context:This series alternates between multiplication and division by simple constants. Recognizing the two-step loop allows a quick computation of the next term from the last known value.

Given Data / Assumptions:

• Series: 8, 24, 12, 36, 18, 54, ...
• Observed operations: ×3, ÷2, ×3, ÷2, ...

Concept / Approach:From any term to the next: if the previous step was ×3, the next is ÷2, and vice versa. Apply the operation appropriate after 54 (which followed a ×3 from 18) — therefore divide by 2.

Step-by-Step Solution:8 → 24: ×3.24 → 12: ÷2.12 → 36: ×3.36 → 18: ÷2.18 → 54: ×3.54 → next: ÷2 ⇒ 27.

Verification / Alternative check:Continuing further would give 27 → 81 (×3) and then 81 → 40.5 (÷2), maintaining the loop. The identified step is consistent.

Why Other Options Are Wrong:108 or 72 correspond to applying ×2 or ×4 rather than ÷2; 68 and 30 do not match the established pattern.

Common Pitfalls:Missing the alternation and applying the same operation repeatedly. Always confirm the last two transitions to detect the loop.

Final Answer:27