Find the wrong number in an alt ×1.5 and ÷3 pattern: 36, 54, 18, 27, 9, 18.5, 4.5

Introduction / Context:
This alternating series multiplies by 1.5 (i.e., ×3/2) and then divides by 3, repeating the two-step cycle. One term fails to obey the cycle and becomes the odd man out.

Given Data / Assumptions:

• Sequence: 36, 54, 18, 27, 9, 18.5, 4.5.
• Hypothesized cycle: ×1.5, ÷3, ×1.5, ÷3, …

Concept / Approach:
Apply the cycle step-by-step. Any value that does not match the computed result under the cycle is the erroneous term.

Step-by-Step Solution:
36 × 1.5 = 54 ✓54 ÷ 3 = 18 ✓18 × 1.5 = 27 ✓27 ÷ 3 = 9 ✓9 × 1.5 = 13.5 (but given: 18.5 ✗)13.5 ÷ 3 = 4.5 (final term is consistent if the prior were corrected)

Verification / Alternative check:
Correcting 18.5 to 13.5 produces the perfectly alternating sequence: 36, 54, 18, 27, 9, 13.5, 4.5.

Why Other Options Are Wrong:

• 54 / 18 / 4.5 each results directly from the stipulated ×1.5 or ÷3 step.

Common Pitfalls:

• Mistaking an average multiplier; ensure alternation is respected (multiply then divide).

Final Answer:
18.5