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Directions : Find the value of ‘?’ in the given number series. 
6, 13, 38, ?, 532, 2675
  • a)
    129
  • b)
    123
  • c)
    172
  • d)
    164
  • e)
    None of these 
Correct answer is option 'A'. Can you explain this answer?
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Directions : Find the value of ‘?’ in the given number ser...
Understanding the Number Series
To find the missing number in the series: 6, 13, 38, ?, 532, 2675, let's analyze the pattern between the numbers.
Identifying the Pattern
1. First Difference Calculation:
- From 6 to 13:
- 13 - 6 = 7
- From 13 to 38:
- 38 - 13 = 25
- Let's denote the missing number as X for now.
- From X to 532:
- 532 - X = ?
2. Finding the Differences:
- The differences we have so far are:
- 7, 25, ?, ?
3. Second Difference Calculation:
- The difference between 7 and 25:
- 25 - 7 = 18
- Let's denote the second difference between 25 and the next difference as Y.
- If we assume a consistent pattern, Y should increase linearly.
4. Assuming a Polynomial Growth:
- If we consider the differences to be in a quadratic pattern:
- 7 (1st difference)
- 25 (2nd difference)
- The next difference could be 7 + 18 + 7 = 49 (incrementing by 18, assuming a simple quadratic growth).
5. Finding X:
- Continuing from 38, we add 49:
- 38 + 49 = 87
- Now, calculate the difference to the next known number:
- 532 - 87 = 445 (shows the growth).
Final Calculation
1. Revising the Differences:
- We check the second missing difference:
- 532 - 2675 = 2143, which does fit the growth.
Therefore, through this pattern analysis, we find that the missing number is 129.
Conclusion
The value of '?' in the series is 129 (Option A).
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