Number Series, Coding, Odd Man OutPYQ June 19Question 2161 of 217
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Find odd one 4,12,44,176,890...\displaystyle 4, 12, 44, 176, 890...

Options

A4
B12
C44
D176
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Correct Answer

✅ Option c — 44

All Options:

  • A4
  • B12
  • C44
  • D176

Detailed Solution & Explanation

Let's find the mathematical rule linking consecutive terms in the series starting with T1=4\displaystyle T_1 = 4:
- T2=T1×2+4=4×2+4=12\displaystyle T_2 = T_1 \times 2 + 4 = 4 \times 2 + 4 = 12
- If the pattern of multiplying by consecutive integers and adding consecutive even integers (+4,+6,+8,+10\displaystyle +4, +6, +8, +10) is followed:
T3=T2×3+6=12×3+6=42T_3 = T_2 \times 3 + 6 = 12 \times 3 + 6 = 42
T4=T3×4+8=42×4+8=168+8=176T_4 = T_3 \times 4 + 8 = 42 \times 4 + 8 = 168 + 8 = 176
T5=T4×5+10=176×5+10=880+10=890T_5 = T_4 \times 5 + 10 = 176 \times 5 + 10 = 880 + 10 = 890

This pattern (Tn=Tn−1×n+2n\displaystyle T_n = T_{n-1} \times n + 2n) is perfectly consistent for all terms except 44\displaystyle 44, which should be 42\displaystyle 42.

Therefore, 44\displaystyle 44 is the incorrect/odd term in the series.

Hence, **Option C** is the correct answer.

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