Number Series, Coding, Odd Man OutMTP June 22Question 2060 of 217
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Find missing term of the series 2,3,3.5,10,13,?,33,172,177\displaystyle 2, 3, 3.5, 10, 13, ?, 33, 172, 177

Options

A23\displaystyle 23
B38\displaystyle 38
C39\displaystyle 39
D40\displaystyle 40
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Correct Answer

✅ Option c — 39\displaystyle 39

All Options:

  • A23\displaystyle 23
  • B38\displaystyle 38
  • C39\displaystyle 39
  • D40\displaystyle 40

Detailed Solution & Explanation

To solve the series 2,3,3.5,10,13,?,33,172,177\displaystyle 2, 3, 3.5, 10, 13, ?, 33, 172, 177, we must first identify and clarify two significant typographical errors in the textbook's problem statement:
1. The numbers 3\displaystyle 3 and 5\displaystyle 5 were erroneously merged and printed as a single decimal 3.5\displaystyle 3.5.
2. The number 43\displaystyle 43 was incorrectly printed as 33\displaystyle 33.

With these corrections, the true logical sequence is:
2,3,3,5,10,13,?,43,172,1772, 3, 3, 5, 10, 13, ?, 43, 172, 177
Let us analyze the logical pattern, which alternates between addition and multiplication with a step-wise increasing integer (+1,×1,+2,×2,+3,×3,+4,×4,+5\displaystyle +1, \times 1, +2, \times 2, +3, \times 3, +4, \times 4, +5):

- T1=2\displaystyle T_1 = 2
- T2=2+1=3\displaystyle T_2 = 2 + 1 = 3
- T3=3×1=3\displaystyle T_3 = 3 \times 1 = 3
- T4=3+2=5\displaystyle T_4 = 3 + 2 = 5 (printed as 3.5\displaystyle 3.5 together with T3\displaystyle T_3)
- T5=5×2=10\displaystyle T_5 = 5 \times 2 = 10
- T6=10+3=13\displaystyle T_6 = 10 + 3 = 13
- T7=13×3=39\displaystyle T_7 = 13 \times 3 = 39 (the missing term)
- T8=39+4=43\displaystyle T_8 = 39 + 4 = 43 (printed as 33\displaystyle 33 due to a typo)
- T9=43×4=172\displaystyle T_9 = 43 \times 4 = 172
- T10=172+5=177\displaystyle T_{10} = 172 + 5 = 177

This mathematical logic perfectly explains every term of the sequence. Therefore, the missing term is 39\displaystyle 39.

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

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