In the number series 380, 188, 92, 48, 20, 8, 2, exactly one term is wrong. Identify the term that does not follow the correct pattern.

Introduction / Context:
The series 380, 188, 92, 48, 20, 8, 2 contains one incorrect term. The numbers are decreasing and the drops between them get smaller in a structured way. A good way to tackle such a question is to inspect the sequence of differences and see whether they follow a regular pattern such as halving.

Given Data / Assumptions:

• Series: 380, 188, 92, 48, 20, 8, 2.
• Exactly one term is incorrect.
• We expect the differences between terms to follow a simple rule.

Concept / Approach:
We compute consecutive differences and try to fit them into a pattern like repeated division by 2 or a systematic halving of the differences themselves. If nearly all steps fit such a pattern but one does not, the term responsible for that irregular step is the wrong term.

Step-by-Step Solution:
1. Compute the differences as given: 188 - 380 = -192 92 - 188 = -96 48 - 92 = -44 20 - 48 = -28 8 - 20 = -12 2 - 8 = -6 2. The differences are -192, -96, -44, -28, -12, -6. 3. Notice that -192 is double -96. If the pattern was perfect halving at each stage, we would expect -96, -48, -24, -12, -6, and so on. 4. So the intended differences likely are -192, -96, -48, -24, -12, -6. 5. Starting from 380: 380 - 192 = 188 (correct second term). 188 - 96 = 92 (correct third term). 92 - 48 = 44 (but the series shows 48, so here is the mismatch). 6. The next intended term after 92 should be 44, not 48. 7. Continue with the intended pattern: 44 - 24 = 20, 20 - 12 = 8, 8 - 6 = 2. 8. The rest of the terms 20, 8 and 2 align with this corrected sequence. 9. Therefore, 48 is the wrong term; it should have been 44.

Verification / Alternative check:
Corrected series under the halving difference rule: 380, 188, 92, 44, 20, 8, 2. Differences: -192, -96, -48, -24, -12, -6. Each difference is half the previous one, producing a clean and symmetric pattern.

Why Other Options Are Wrong:

• 20, 92, 2: All of these numbers fit naturally into the corrected series and respect the halving of differences. Removing any of them would break the identified pattern.

Common Pitfalls:
Students sometimes focus only on the numbers themselves, trying to find a direct multiplicative relation like repeatedly dividing by 2. That approach does not work well here. Instead, we must look at how much each term decreases compared to the previous term and see whether those decreases themselves follow a pattern.

Final Answer:
The wrong term in the original series is 48.