Number series (alternate ×3 and ÷2 pattern): 8, 24, 12, 36, 18, 54, (…) Find the next term that correctly continues the alternating multiplication/division sequence.

Introduction / Context:Many number series use alternating operations. Recognizing the repeating pattern (multiply by a constant, then divide by a constant) allows quick continuation of the sequence.

Given Data / Assumptions:

• Given terms: 8, 24, 12, 36, 18, 54, (…)
• We suspect an alternating rule between consecutive terms.

Concept / Approach:Compare each transition: 8 to 24 appears as ×3, then 24 to 12 as ÷2. If this alternates, the pattern is ×3, ÷2, ×3, ÷2, and so on.

Step-by-Step Solution:

Verification / Alternative check:Continue one more step mentally to ensure consistency: after 27, the next would be ×3 → 81, reinforcing the alternating structure.

Why Other Options Are Wrong:

• 108 and 72: These would match a ×2 or ×4 step, which breaks the ÷2 requirement at this position.
• 68: Does not match any simple consistent factor with the pattern.

Common Pitfalls:Applying the wrong operation order (e.g., dividing when multiplication is due). Always map the full alternating pattern before computing the next term.

Final Answer:27