Number Series, Coding and DecodingPYQ May 25Question 4340 of 217
All Questions

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

Options

A332
B338
C356
D362
For any discrepancies in this question, email contact@cadada.in

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.

Related Comparison Tables

Cardinal vs Ordinal Utility: Measuring Satisfaction

More Questions from Number Series, Coding and Decoding

The number in place of question mark in: 7,26,63,124,215,?,511\displaystyle 7, 26, 63, 124, 215, ?, 511 is

Find missing term 7,26,63,124,215,342,?\displaystyle 7, 26, 63, 124, 215, 342, ?

Which number should come next 7,26,63,124,215,342,?\displaystyle 7, 26, 63, 124, 215, 342, ?

If CLOCK is coded as 34235 and TIME as 8679, then MOTEL is coded as:

If MOUSE, is coded as 34651 and KEY is coded as 217, then how will YES be coded?

In a certain code language PREMONITION is written as 68530492904\displaystyle 68530492904, how will the word MONITOR be written in that code language?

Ready to Master Number Series, Coding and Decoding?

Practice all 217 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free