Number Series, Coding and DecodingPYQ May 25Question 4341 of 217
All Questions

Find the missing number in the given series: 4, 18 ______, 100, 180, 294, 448

Options

A48
B52
C56
D64
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Correct Answer

✅ Option a — 48

All Options:

  • A48
  • B52
  • C56
  • D64

Detailed Solution & Explanation

Let us analyze the terms of the given series:
4,18,…,100,180,294,4484, 18, \dots, 100, 180, 294, 448
Let\'s test if there is a pattern related to cubes and squares of consecutive integers, such as n3−n2\displaystyle n^3 - n^2:
- For n=2\displaystyle n = 2: 23−22=8−4=4\displaystyle 2^3 - 2^2 = 8 - 4 = 4
- For n=3\displaystyle n = 3: 33−32=27−9=18\displaystyle 3^3 - 3^2 = 27 - 9 = 18
- For n=4\displaystyle n = 4: 43−42=64−16=48\displaystyle 4^3 - 4^2 = 64 - 16 = 48
- For n=5\displaystyle n = 5: 53−52=125−25=100\displaystyle 5^3 - 5^2 = 125 - 25 = 100
- For n=6\displaystyle n = 6: 63−62=216−36=180\displaystyle 6^3 - 6^2 = 216 - 36 = 180
- For n=7\displaystyle n = 7: 73−72=343−49=294\displaystyle 7^3 - 7^2 = 343 - 49 = 294
- For n=8\displaystyle n = 8: 83−82=512−64=448\displaystyle 8^3 - 8^2 = 512 - 64 = 448

This formula matches all the terms of the series exactly. Therefore, the missing term corresponds to the third term (n=4\displaystyle n = 4):
Missing term=43−42=48\text{Missing term} = 4^3 - 4^2 = 48
Hence, **Option A** 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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