Consider the following series of numbers: 2, 5, 10, 50, 500, 5000 Exactly one term does not follow the pattern of the series. Identify the term that is wrong.

Introduction / Context:
This is a 'wrong term' number series question. All but one of the terms follow a simple pattern, and one term breaks that pattern. The task is to discover the underlying rule that governs most of the sequence and then identify the outlier that does not conform to that rule.

Given Data / Assumptions:

• Series: 2, 5, 10, 50, 500, 5000.
• Exactly one term is incorrect or inconsistent.
• We must find which term breaks the pattern.
• Options: 5000, 500, 10, 50.

Concept / Approach:
Rather than assuming a simple geometric progression, we can look at how each term might depend on the previous two. For middle terms in a six-term series, it is common that each new term is formed by multiplying the previous two terms. If that relationship holds for most of the sequence but fails at one position, that failing term is the wrong one.

Step-by-Step Solution:
Step 1: Check the product of each pair of consecutive terms. Step 2: For the third term: 2 × 5 = 10, which matches the third term. Step 3: For the fourth term: 5 × 10 = 50, which matches the fourth term. Step 4: For the fifth term: 10 × 50 = 500, which matches the fifth term. Step 5: Extend the same rule to predict the sixth term: the next term should be 50 × 500 = 25000. Step 6: However, the given sixth term is 5000, not 25000, so the sixth term clearly breaks the pattern.

Verification / Alternative check:
Notice that the rule 'each term from the third onwards equals the product of the previous two terms' holds perfectly for the third, fourth and fifth terms. There is no need to adjust this clean and simple rule, which strongly indicates that the failure is at the last term rather than earlier in the series.

Why Other Options Are Wrong:
If we mark 10, 50 or 500 as wrong, the product-of-previous-two rule fails at an earlier step. For example, if 10 were wrong, 2 × 5 would not yield the third term; if 50 were wrong, 5 × 10 would not equal the fourth term, and similarly for 500. Since the rule works perfectly for these terms, they are consistent with the intended pattern and should not be removed.

Common Pitfalls:
Test-takers often look only at simple ratios, such as 5/2, 10/5, 50/10 and so on, and may be confused by the changing multipliers. Focusing on the relationship between consecutive pairs of terms and exploring whether the next term might be their product is a more effective strategy in such 'wrong term' questions.

Final Answer:
The only term that does not fit the rule 'each term equals the product of the previous two terms' is the last one, 5000, so option (a) is the correct answer.