Select the number from among the given options that can replace the question mark (?) in the following series. 80, 73, 64, 53, 40, ?
25
Solving the Number Series Pattern
The given number series is 80, 73, 64, 53, 40, ?. We need to find the number that replaces the question mark by identifying the pattern in the series.
Analyzing the Differences
Let's find the difference between consecutive terms in the series:
- Difference between the 1st and 2nd term: $80 - 73 = 7$
- Difference between the 2nd and 3rd term: $73 - 64 = 9$
- Difference between the 3rd and 4th term: $64 - 53 = 11$
- Difference between the 4th and 5th term: $53 - 40 = 13$
Identifying the Pattern in Differences
The differences between consecutive terms are 7, 9, 11, 13. We can observe that these differences form a sequence of consecutive odd numbers starting from 7. The pattern is that each subsequent difference increases by 2.
Pattern of differences: +2, +2, +2 ...
- $9 - 7 = 2$
- $11 - 9 = 2$
- $13 - 11 = 2$
Predicting the Next Difference
Following this pattern, the next difference should be the next odd number after 13, which is $13 + 2 = 15$.
Calculating the Next Term
To find the next term in the original series (replacing the question mark), we subtract the next difference (15) from the last known term (40):
Next term = $40 - 15$
Next term = $25$
So, the number that replaces the question mark is 25.
Conclusion
The series follows a pattern where the difference between consecutive terms is a sequence of increasing odd numbers (7, 9, 11, 13, 15, ...). The next term in the series is 25.
| Series Term | 80 | 73 | 64 | 53 | 40 | ? |
| Difference | -7 | -9 | -11 | -13 | -15 |
Revision Table: Number Series Patterns
| Pattern Type | Description | Example |
|---|---|---|
| Arithmetic Series | Constant difference between terms. | 2, 5, 8, 11, ... (difference is 3) |
| Geometric Series | Constant ratio between terms. | 3, 6, 12, 24, ... (ratio is 2) |
| Difference Series | The differences between terms follow a pattern (like arithmetic, geometric, or odd/even numbers). | The series solved here (differences 7, 9, 11, 13, ...) |
| Mixed Series | Combination of different patterns or operations. | 1, 3, 7, 15, 31, ... (pattern is multiply by 2, add 1) |
Additional Information: Solving Quantitative Aptitude Series
Number series questions are common in quantitative aptitude tests. To solve them effectively:
- Always start by finding the difference or ratio between consecutive terms.
- Look for patterns in the differences/ratios (arithmetic progression, geometric progression, perfect squares, cubes, prime numbers, odd/even numbers).
- Sometimes, the pattern might involve alternating differences or a combination of operations (like multiply and add/subtract).
- Practice with various types of series to recognize common patterns quickly.
- If differences don't show a clear pattern, calculate the differences of the differences (second-order differences).
Understanding these techniques helps in quickly identifying the underlying rule governing the sequence and finding the missing term.
Similar Questions
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Important Questions from Number Series
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A series is given with one term wrong. Select that wrong term from the given alternatives.
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