Number Series, Coding and DecodingPYQ May 25Question 4040 of 217
All Questions

Identify the next number in the following series: 2, 8, 26, 62, 122, 212, _______

Options

A332
B338
C356
D362
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Correct Answer

✅ Option b — 338

All Options:

  • A332
  • B338
  • C356
  • D362

Detailed Solution & Explanation

Let the terms of the series be denoted by T1,T2,T3,…\displaystyle T_1, T_2, T_3, \dots
The given series is:
2,8,26,62,122,212,…2, 8, 26, 62, 122, 212, \dots
Let\'s find the first differences between consecutive terms:
- T2−T1=8−2=6\displaystyle T_2 - T_1 = 8 - 2 = 6
- T3−T2=26−8=18\displaystyle T_3 - T_2 = 26 - 8 = 18
- T4−T3=62−26=36\displaystyle T_4 - T_3 = 62 - 26 = 36
- T5−T4=122−62=60\displaystyle T_5 - T_4 = 122 - 62 = 60
- T6−T5=212−122=90\displaystyle T_6 - T_5 = 212 - 122 = 90
The first differences are: 6,18,36,60,90\displaystyle 6, 18, 36, 60, 90.

Now, let\'s find the differences of these 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: 12,18,24,30\displaystyle 12, 18, 24, 30.
We can see that the second differences increase by 6\displaystyle 6 each time (forming an Arithmetic Progression with common difference 6\displaystyle 6).

Following this pattern, the next second difference should be:
30+6=3630 + 6 = 36
Therefore, the next first difference should be:
90+36=12690 + 36 = 126
Thus, the next term in the series (T7\displaystyle T_7) will be:
T7=212+126=338T_7 = 212 + 126 = 338
Hence, **Option B** 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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