Number series – find the wrong term (identify the outlier) Series: 6, 15, 35, 77, 165, 221

Introduction / Context:
This aptitude problem asks you to detect the single wrong term (outlier) in a numeric series. Such questions test recognition of a hidden rule (often multiplicative or additive patterns) and the ability to verify each term consistently.

Given Data / Assumptions:

• Series shown: 6, 15, 35, 77, 165, 221.
• Exactly one term is incorrect.
• We must infer the intended rule and spot the inconsistent term.

Concept / Approach:
Look for a recurring operation. A common pattern is “double the previous term and add consecutive odd numbers”. We test whether each transition follows: next = previous * 2 + an odd number that increases by 2 each time (… +3, +5, +7, +9, +11, …).

Step-by-Step Solution:

Verification / Alternative check:
Try to fit 221 using the same rule: the only way would be 1652 + x = 221 ⇒ x = -109 (not an odd positive step). Hence 221 is inconsistent.

Why Other Options Are Wrong:

• 15, 35, 77, 165 all align with doubling and adding a small odd number in sequence; they can be reconciled with the intended pattern.

Common Pitfalls:
Mistaking a near-miss as the wrong term without checking subsequent implications; not projecting the rule beyond one step to verify consistency.

Final Answer:
221