Number Series, Coding and DecodingPYQ Sept 25Question 4140 of 217
All Questions

Complete the given series: 0, 6, 24, 60, 120, 210,

Options

A240
B290
C336
D504
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Correct Answer

✅ Option c — 336

All Options:

  • A240
  • B290
  • C336
  • D504

Detailed Solution & Explanation

Let us analyze the terms of the series: 0,6,24,60,120,210,…\displaystyle 0, 6, 24, 60, 120, 210, \dots
Let us find the differences between consecutive terms: - 6−0=6\displaystyle 6 - 0 = 6 - 24−6=18\displaystyle 24 - 6 = 18 - 60−24=36\displaystyle 60 - 24 = 36 - 120−60=60\displaystyle 120 - 60 = 60 - 210−120=90\displaystyle 210 - 120 = 90
Let us look at the differences of the differences (second differences): - 18−6=12\displaystyle 18 - 6 = 12 - 36−18=18\displaystyle 36 - 18 = 18 - 60−36=24\displaystyle 60 - 36 = 24 - 90−60=30\displaystyle 90 - 60 = 30 The second differences are increasing by 6 each time. So the next second difference should be: 30+6=3630 + 6 = 36
This means the next first difference should be: 90+36=12690 + 36 = 126
Thus, the next term of the series is: 210+126=336210 + 126 = 336
Alternatively, the general term of the series can be written as Tn=n3−n\displaystyle T_n = n^3 - n: - For n=1\displaystyle n = 1: 13−1=0\displaystyle 1^3 - 1 = 0 - For n=2\displaystyle n = 2: 23−2=6\displaystyle 2^3 - 2 = 6 - For n=3\displaystyle n = 3: 33−3=24\displaystyle 3^3 - 3 = 24 - For n=4\displaystyle n = 4: 43−4=60\displaystyle 4^3 - 4 = 60 - For n=5\displaystyle n = 5: 53−5=120\displaystyle 5^3 - 5 = 120 - For n=6\displaystyle n = 6: 63−6=210\displaystyle 6^3 - 6 = 210 - For n=7\displaystyle n = 7: 73−7=343−7=336\displaystyle 7^3 - 7 = 343 - 7 = 336 This confirms the next term is 336.
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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