Number Series, Coding and DecodingMCQMTP June 22Question 2060 of 217
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Find missing term of the series $2, 3, 3.5, 10, 13, ?, 33, 172, 177$

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option c — $39$

All Options:

  • A$23$
  • B$38$
  • C$39$
  • D$40$

Detailed Solution & Explanation

To solve the series $2, 3, 3.5, 10, 13, ?, 33, 172, 177,wemustfirstidentifyandclarifytwosignificanttypographicalerrorsinthetextbook′sproblemstatement:<br>1.Thenumbers\displaystyle , we must first identify and clarify two significant typographical errors in the textbook's problem statement:<br>1. The numbers3and\displaystyle and5$ were erroneously merged and printed as a single decimal $3.5$.
2. The number $43$ was incorrectly printed as $33$.

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, ×\displaystyle \times 1, +2, ×\displaystyle \times 2, +3, ×\displaystyle \times 3, +4, ×\displaystyle \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 ×\displaystyle \times 1 = 3
- T4=3+2=5\displaystyle T_4 = 3 + 2 = 5 (printed as $3.5togetherwith\displaystyle together withT_3)<br>−\displaystyle )<br>-T_5 = 5 ×\displaystyle \times 2 = 10<br>−\displaystyle <br>-T_6 = 10 + 3 = 13<br>−\displaystyle <br>-T_7 = 13 ×\displaystyle \times 3 = 39(themissingterm)<br>−\displaystyle (the missing term)<br>-T_8 = 39 + 4 = 43$ (printed as $33$ due to a typo)
- T9=43×4=172\displaystyle T_9 = 43 ×\displaystyle \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 $39$.

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

About This Chapter: Number Series, Coding and Decoding

Paper

Paper 3: Quantitative Aptitude

Weightage

5 Marks

Key Topics

Number series, Coding & Decoding, Odd man out

This chapter covers Number series, Coding & Decoding, Odd man out and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 5 Marks weightage. Focus on understanding core concepts rather than memorizing.

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