In the number sequence 36, 54, 18, 27, 9, 18.5, 4.5, which single term is incorrect and breaks the alternating multiply-and-divide pattern?

Introduction / Context:
This series question involves alternating multiplication and division by simple fractions. The goal is to detect that pattern and then identify the single term that does not follow it. Such questions strengthen your understanding of fractional operations and pattern recognition.

Given Data / Assumptions:
The sequence is: 36, 54, 18, 27, 9, 18.5, 4.5. We assume that the intended pattern uses simple ratios, such as multiplying by 3/2 or dividing by 3, and that exactly one term is incorrect.

Concept / Approach:
Because the numbers go up and down, an alternating pattern is likely: multiply by a fixed factor, then divide by another fixed factor, and so on. The simplest ratio to test here is 3/2 (which is 1.5) for multiplication and 3 for division, since 36 to 54 suggests multiplication by 3/2, and 54 to 18 suggests division by 3.

Step-by-Step Solution:
Step 1: Check the first few transitions.36 → 54: 36 * (3/2) = 36 * 1.5 = 54.54 → 18: 54 / 3 = 18.18 → 27: 18 * (3/2) = 27.27 → 9: 27 / 3 = 9.Step 2: Up to this point, the pattern is clear: multiply by 3/2, then divide by 3, and repeat.Step 3: Continue the same pattern: 9 * (3/2) = 9 * 1.5 = 13.5 (not 18.5). Then 13.5 / 3 = 4.5.Step 4: The last term 4.5 is consistent with the pattern if we use 13.5 in place of 18.5. Therefore, 18.5 is the only number that does not fit the intended rule.

Verification / Alternative check:
Write the ideal pattern explicitly: 36, 54, 18, 27, 9, 13.5, 4.5, where the operations are *3/2, /3, *3/2, /3, *3/2, /3. Every transition satisfies either multiplying by 1.5 or dividing by 3. The given sequence breaks this rule only once, at the position where 18.5 appears instead of 13.5. Hence 18.5 is clearly the wrong term.

Why Other Options Are Wrong:
36, 27 and 9 all satisfy the multiply-by-3/2 or divide-by-3 rule when placed in the correct positions. Changing any of them would destroy multiple correct transitions and would not restore a neat alternating pattern, so they cannot be the unique culprit.

Common Pitfalls:
Some learners may only compare each term with its immediate neighbor, without spotting the alternating nature of the operations. Others may try to fit a single operation (only multiplication or only division) which will not work. Remember to consider repeating cycles such as multiply then divide in series questions.

Final Answer:
The incorrect term that breaks the multiply-by-3/2, divide-by-3 pattern is 18.5.