Find the missing value in the series: 51, 52, 60, 87, 151, . 492.

Option b: 276. Solution: To find the missing value in the series 51, 52, 60, 87, 151, ?, 492 , let us analyze the differences between consecutive terms: - 1st to 2nd term: 52 - 51 = 1 = 13 - 2nd to 3rd term: 60 - 52 = 8 = 23 - 3rd to 4th term: 87 - 60 = 27 = 33 - 4th to 5th term: 151 - 87 = 64 = 43 We observe that the difference between terms is the sequence of consecutive perfect cubes ( 13, 23, 33, 43, ... ). Following this logical pattern, the next difference must be 53 = 125 . We add 125 to the 5th term ( 151 ): 151 + 125 = 276 Let us verify the final step by adding 63 = 216 to our result: 276 + 216 = 492 This perfectly matches the last term in the sequence, mathematically proving that the missing term is 276 . Hence, Option B is the correct answer.

Find the missing value in the series: $51, 52, 60, 87, 151, ______. 492.$

The correct answer is Option b: $276$. To find the missing value in the series $51, 52, 60, 87, 151, ?, 492$, let us analyze the differences between consecutive terms: - 1st to 2nd term: $52 - 51 = 1 = 1^3$ - 2nd to 3rd term: $60 - 52 = 8 = 2^3$ - 3rd to 4th term: $87 - 60 = 27 = 3^3$ - 4th to 5th term: $151 - 87 = 64 = 4^3$ We observe that the difference between terms is the sequence of consecutive perfect cubes ($1^3, 2^3, 3^3, 4^3, \dots$). Following this logical pattern, the next difference must be $5^3 = 125$. We add $125$ to the 5th term ($151$): $$151 + 125 = 276$$ Let us verify the final step by adding $6^3 = 216$ to our result: $$276 + 216 = 492$$ This perfectly matches the last term in the sequence, mathematically proving that the missing term is $276$. Hence, **Option B** is the correct answer.

Number Series, Coding and DecodingMCQMTP Sep 24 Series IQuestion 2079 of 217

All Questions

Find the missing value in the series: $\displaystyle 51, 52, 60, 87, 151, ______. 492.$

Options

\displaystyle 195

\displaystyle 276

\displaystyle 317

\displaystyle 420

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option b — $\displaystyle 276$

All Options:

A $\displaystyle 195$
B $\displaystyle 276$
C $\displaystyle 317$
D $\displaystyle 420$

Detailed Solution & Explanation

To find the missing value in the series

\displaystyle 51, 52, 60, 87, 151, ?, 492

, let us analyze the differences between consecutive terms:

- 1st to 2nd term:

\displaystyle 52 - 51 = 1 = 1^3

- 2nd to 3rd term:

\displaystyle 60 - 52 = 8 = 2^3

- 3rd to 4th term:

\displaystyle 87 - 60 = 27 = 3^3

- 4th to 5th term:

\displaystyle 151 - 87 = 64 = 4^3

We observe that the difference between terms is the sequence of consecutive perfect cubes (

\displaystyle 1^3, 2^3, 3^3, 4^3, \dots

).
Following this logical pattern, the next difference must be

\displaystyle 5^3 = 125

. We add

\displaystyle 125

to the 5th term (

\displaystyle 151

151 + 125 = 276

Let us verify the final step by adding

\displaystyle 6^3 = 216

to our result:

276 + 216 = 492

This perfectly matches the last term in the sequence, mathematically proving that the missing term is

\displaystyle 276

.

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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Find the missing value in the series: \displaystyle 51, 52, 60, 87, 151, ______. 492.