In the series 5, 15, 30, 80, 180, 540, 1080, which term is incorrect and should be considered the wrong number?

Introduction / Context:
This question is from the odd man out or wrong term in series category. The goal is to detect a consistent pattern that most terms follow and then identify the term that violates that pattern. Such problems measure logical reasoning and attention to multiplicative patterns in number sequences.

Given Data / Assumptions:
- The sequence is 5, 15, 30, 80, 180, 540, 1080.
- Exactly one term is wrong and does not follow the main pattern.
- All other terms fit a simple multiplicative rule.
- We need to find which term breaks that rule.

Concept / Approach:
In many numeric series, terms are obtained by multiplying the previous term by alternating constants, often 2 and 3. Here, the numbers grow quickly, which suggests a pattern involving repeated multiplication. We will examine ratios of consecutive terms to see whether they follow a regular pattern such as multiply by 3, then by 2, and so on.

Step-by-Step Solution:
Step 1: Compute ratios of consecutive terms. 15 / 5 = 3. 30 / 15 = 2. 80 / 30 ≈ 2.67 (not a simple integer factor). 180 / 80 = 2.25. 540 / 180 = 3. 1080 / 540 = 2. Step 2: Guess the intended pattern. A very natural intended pattern is multiply alternately by 3 and 2. Starting from 5, we get: 5 * 3 = 15, then 15 * 2 = 30. If we follow this, the next term should be 30 * 3 = 90, not 80. Then 90 * 2 = 180, 180 * 3 = 540, and 540 * 2 = 1080. Step 3: Identify the wrong term. Only the term 80 breaks the alternating multiply by 3, then multiply by 2 pattern.

Verification / Alternative check:
Construct the corrected series using the intended pattern: 5, 15, 30, 90, 180, 540, 1080. Now check the ratios: 15 / 5 = 3, 30 / 15 = 2, 90 / 30 = 3, 180 / 90 = 2, 540 / 180 = 3, 1080 / 540 = 2. The pattern multiply by 3, then by 2 repeats perfectly, confirming that 80 is the only inconsistent value.

Why Other Options Are Wrong:
Option A (540) fits the pattern as 180 * 3 = 540.
Option B (180) is correct because 90 * 2 = 180 in the intended series.
Option C (30) is also correct since 15 * 2 = 30.
Option D (80) is the only number that does not equal the previous term multiplied by 3 or 2 in the correct order, so it must be the wrong term.

Common Pitfalls:
Students sometimes focus only on differences rather than ratios and fail to notice the multiplicative pattern. Another mistake is to accept approximate non integer ratios such as 2.67 and 2.25 and assume the question is about arbitrary growth instead of a neat alternating rule. Always test both addition and multiplication based patterns and look for the simplest consistent explanation that fits most terms.

Final Answer:
The wrong term in the series is 80.