Number series – find the incorrect term: 15, 16, 34, 105, 424, 2124, 12756

Introduction / Context:This problem tests recognition of multiplicative patterns with a small additive tweak in an integer sequence. Your goal is to detect which term breaks the otherwise consistent rule governing the series.

Given Data / Assumptions:

• Series: 15, 16, 34, 105, 424, 2124, 12756
• Exactly one term is wrong.
• Operations may involve multiplying by a changing factor and adding a matching increment.

Concept / Approach:

Look for a pattern such as “multiply by n, then add n” where n increases by 1 each step. This type of linear-increment multiplier pattern is common in reasoning tests.

Step-by-Step Solution:

Verification / Alternative check:

All transitions obey the rule multiply-by-n then add n (n = 1, 2, 3, 4, 5, 6) except the given 2124. Replacing it with 2125 restores perfect consistency.

Why Other Options Are Wrong:

16, 34, 105, 424, and 12756 each exactly satisfy the rule with their neighbors, so they are not erroneous.

Common Pitfalls:

Trying constant differences or ratios will mislead; the key is the steadily increasing multiplier and the matched addend.

Final Answer:

2124