Find the Wrong (Odd) Term

🎯 Learning Objective

Detect the single term that breaks an otherwise perfect pattern and state its correct value.

💡 Concept

• First establish the rule from the terms that clearly agree, then test every term against it.
• The wrong term is the one value that does not fit the confirmed rule.
• Often the surrounding terms are correct, so the pattern is visible on both sides of the error.
• Re-derive the correct term to double-check you found the true odd one out.
• Common bases for wrong-term series: powers of 2, ×2+1 rules, n²−1, and constant differences.

🧮 Key Formulas

Confirm rule from majority of terms, then flag the misfit

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Correct term = value the rule actually demands

✏️ Easy Example

Q. Find the wrong term: 2, 4, 8, 16, 30, 64

1. These look like powers of 2: 2, 4, 8, 16, 32, 64
2. The 5th term should be 32, not 30

Answer: 30 is wrong (it should be 32)

🇮🇳 Real-Life Example

A ticket-checker scanning seat numbers spots the one out-of-sequence berth instantly — wrong-term problems train exactly that 'which one does not belong' reflex.

📝 Exam-Level Example

Q. Find the wrong term: 3, 8, 15, 24, 34, 48, 63

1. Test n² − 1: 2²−1=3, 3²−1=8, 4²−1=15, 5²−1=24, 6²−1=35, 7²−1=48, 8²−1=63
2. The 5th term should be 35, but the series shows 34

Answer: 34 is wrong (it should be 35)

📝 Exam-Level Example

Q. Find the wrong term: 5, 11, 23, 47, 95, 190

1. Test ×2 + 1: 5×2+1=11, 11×2+1=23, 23×2+1=47, 47×2+1=95, 95×2+1=191
2. The last term should be 191, but the series shows 190

Answer: 190 is wrong (it should be 191)

🪄 Memory Trick

Nail the rule using the first two or three terms, then walk forward. The first term that disagrees is your answer — and re-computing it confirms the fix.

⚠️ Common Mistakes

• ❌ Assuming the FIRST term is wrong without confirming the rule from later terms
• ❌ Stopping at 'it feels off' without computing the correct value
• ❌ Changing the rule to fit the wrong term instead of flagging it

🏆 Exam Tips

• ✅ Let the majority of terms decide the rule, not a single suspicious one
• ✅ Always state BOTH the wrong term and its correct value

📌 Summary

• Fix the rule from agreeing terms first
• Test each term; the misfit is the answer
• Re-derive the correct value to confirm
• Watch bases: powers, ×2+1, n²−1, constant d