Find the wrong term in the number series: 108, 54, 36, 18, 9, 6, 4. Exactly one term violates an alternating division pattern; identify the incorrect term.

Introduction / Context:We seek a neat, alternating multiplier/divisor pattern and then detect the unique violation in the sequence.

Given Data / Assumptions:

• Series: 108, 54, 36, 18, 9, 6, 4.
• Try alternating operations such as ÷2 and ×2/3 (equivalently, multiply by 0.5 and 0.6667).

Concept / Approach:Compute consecutive ratios to test the alternating rule: 108→54 (×0.5), 54→36 (×2/3), 36→18 (×0.5), next should be 18×(2/3)=12, and so on.

Step-by-Step Solution:

Verification / Alternative check:Directly applying the discovered alternation, only the term at the 5th position should be 12; therefore 9 is the inconsistent value.

Why Other Options Are Wrong:54, 36, 18 match the alternation before the error; the final terms often look close but are consequences of carrying the wrong intermediate value.

Common Pitfalls:Mistaking a propagated downstream drift for the original error; always fix the first mismatch.

Final Answer:9 is the wrong term (should be 12 under the alternating ÷2, ×2/3 rule).