Number Series, Coding and DecodingMCQMTP Dec 22 Series IIQuestion 2065 of 217
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Find the missing term of the following series: 7,26,63,124,215,342?\displaystyle 7, 26, 63, 124, 215, 342?

Options

A391\displaystyle 391
B421\displaystyle 421
C481\displaystyle 481
D511\displaystyle 511
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Correct Answer

✅ Option d — 511\displaystyle 511

All Options:

  • A391\displaystyle 391
  • B421\displaystyle 421
  • C481\displaystyle 481
  • D511\displaystyle 511

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Detailed Solution & Explanation

To find the missing term of the series 7,26,63,124,215,342,?\displaystyle 7, 26, 63, 124, 215, 342, ?, let us analyze the relation of each term to perfect cubes:

- 1st term: 23−1=8−1=7\displaystyle 2^3 - 1 = 8 - 1 = 7
- 2nd term: 33−1=27−1=26\displaystyle 3^3 - 1 = 27 - 1 = 26
- 3rd term: 43−1=64−1=63\displaystyle 4^3 - 1 = 64 - 1 = 63
- 4th term: 53−1=125−1=124\displaystyle 5^3 - 1 = 125 - 1 = 124
- 5th term: 63−1=216−1=215\displaystyle 6^3 - 1 = 216 - 1 = 215
- 6th term: 73−1=343−1=342\displaystyle 7^3 - 1 = 343 - 1 = 342

Following this logical pattern, the next term must be:
- 7th term: 83−1=512−1=511\displaystyle 8^3 - 1 = 512 - 1 = 511

Therefore, the mathematical answer is **511\displaystyle 511**, which corresponds to **Option D**.

*Note on Answer Key Discrepancy:* The textbook/exam answer key lists **Option B** (421\displaystyle 421) as the correct answer. However, 421\displaystyle 421 does not correspond to any logical progression of the series, while 511\displaystyle 511 perfectly completes the cubic pattern n3−1\displaystyle n^3 - 1. This is a confirmed typographical error in the official answer key, and the mathematically correct option is **Option D**.

Hence, **Option D** 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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