Select the number from among the given options that can replace the question mark (?) in the following series. 34, 37, 42, 49, 60, 73, 90, ?
109
Solving the Given Number Series
The question asks us to find the next number in the series: 34, 37, 42, 49, 60, 73, 90, ?
To solve a number series problem, we typically look for a pattern in the terms or the differences between consecutive terms.
Analyzing the Differences Between Terms
Let's calculate the difference between each term and the previous one:
- The difference between the 2nd term (37) and the 1st term (34) is: 37 - 34 = 3
- The difference between the 3rd term (42) and the 2nd term (37) is: 42 - 37 = 5
- The difference between the 4th term (49) and the 3rd term (42) is: 49 - 42 = 7
- The difference between the 5th term (60) and the 4th term (49) is: 60 - 49 = 11
- The difference between the 6th term (73) and the 5th term (60) is: 73 - 60 = 13
- The difference between the 7th term (90) and the 6th term (73) is: 90 - 73 = 17
The sequence of differences we found is: 3, 5, 7, 11, 13, 17.
Identifying the Pattern in the Differences
Let's examine the sequence of differences: 3, 5, 7, 11, 13, 17.
These numbers are prime numbers. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
The sequence 3, 5, 7, 11, 13, 17 is the sequence of prime numbers starting from 3.
Following this pattern, the next difference must be the next prime number after 17, which is 19.
Calculating the Next Term
To find the next term in the original series, we add the next difference (19) to the last term given in the series (90).
Next term = Last term + Next difference
Next term = 90 + 19 = 109
Conclusion: The Missing Number
Based on the pattern of prime number differences, the number that replaces the question mark is 109.
Revision Table: Number Series Analysis
| Term Position | Term Value | Difference from Previous | Pattern Observed |
|---|---|---|---|
| 1st | 34 | - | - |
| 2nd | 37 | 37 - 34 = 3 | Prime (3rd) |
| 3rd | 42 | 42 - 37 = 5 | Prime (4th) |
| 4th | 49 | 49 - 42 = 7 | Prime (5th) |
| 5th | 60 | 60 - 49 = 11 | Prime (6th) |
| 6th | 73 | 73 - 60 = 13 | Prime (7th) |
| 7th | 90 | 90 - 73 = 17 | Prime (8th) |
| 8th | 109 | 109 - 90 = 19 | Prime (9th) |
Additional Information: Prime Numbers and Series
Understanding prime numbers is fundamental in solving certain types of number series and reasoning questions. A prime number is a positive integer greater than 1 that has exactly two positive divisors: 1 and itself.
The sequence of prime numbers starts with 2, 3, 5, 7, 11, 13, 17, 19, 23, ...
Number series questions can involve various patterns, including arithmetic progression, geometric progression, differences, differences of differences, squares, cubes, prime numbers, composite numbers, Fibonacci sequence, or a combination of these patterns.
Recognizing the sequence of prime numbers is a common technique required to solve reasoning problems like the one presented here.
Important Questions from Number Series
Select the number from among the given options that can replace the question mark (?) in the following series.
15, 45, 75, 105, ?
Identify the number that does NOT belong to the following series.
18, 27, 35, 45, 54
Select the number from among the given options that can replace the question mark (?) in the following series.
37, 41, 50, 66, ?
दिए गए विकल्पों में से वह संख्या चुनिए जो निम्नलिखित श्रृंखला में प्रश्नवाचक चिन्ह (?) को प्रतिस्थापित कर सके।
20, 21, 25, 34,?, 75
Select the correct option that will fill in the blank and complete the series.
45, 49, 58, 74, .........
