Complete the series.
15
Solving the Number Series: Finding the Missing Term
The question asks us to complete the given number series: 31, 29, 24, 22, 17, (…)
To find the next term in the series, we need to identify the pattern or rule that governs the sequence of numbers.
Identifying the Pattern in the Series
Let's look at the differences between consecutive terms in the series:
- Difference between the 1st and 2nd term: $29 - 31 = -2$
- Difference between the 2nd and 3rd term: $24 - 29 = -5$
- Difference between the 3rd and 4th term: $22 - 24 = -2$
- Difference between the 4th and 5th term: $17 - 22 = -5$
We can see a repeating pattern in the differences: -2, -5, -2, -5. This means the series is generated by alternately subtracting 2 and 5 from the preceding term.
Applying the Pattern to Find the Next Term
The pattern is to subtract 2, then subtract 5, then subtract 2, then subtract 5, and so on.
The last operation performed to get the 5th term (17) from the 4th term (22) was subtracting 5 ($22 - 5 = 17$).
According to the pattern, the next operation to find the 6th term should be subtracting 2 from the 5th term.
So, the next term is: $17 - 2$
$17 - 2 = 15$
Therefore, the next term in the series is 15.
Step-by-Step Calculation
Here's how the series progresses based on the identified pattern:
- Starting term: 31
- $31 - 2 = 29$ (2nd term)
- $29 - 5 = 24$ (3rd term)
- $24 - 2 = 22$ (4th term)
- $22 - 5 = 17$ (5th term)
- $17 - 2 = 15$ (6th term)
The completed series is 31, 29, 24, 22, 17, 15.
| Term Number | Term Value | Operation from Previous Term |
|---|---|---|
| 1 | 31 | - |
| 2 | 29 | $31 - 2$ |
| 3 | 24 | $29 - 5$ |
| 4 | 22 | $24 - 2$ |
| 5 | 17 | $22 - 5$ |
| 6 | 15 | $17 - 2$ |
Conclusion
Based on the pattern of alternating subtractions of 2 and 5, the next term in the series 31, 29, 24, 22, 17 is 15.
Revision Table: Understanding Number Series
| Concept | Description | Example Pattern Types |
|---|---|---|
| Number Series | A sequence of numbers that follow a specific pattern or rule. | Arithmetic, Geometric, Alternating Difference, Fibonacci, etc. |
| Pattern Identification | The process of finding the underlying rule that connects the numbers in the series. This often involves looking at differences, ratios, or operations between terms. | Differences between terms, Ratios between terms, Operations (+, -, ×, ÷) applied sequentially or alternately. |
| Alternating Pattern | A pattern where the operation or rule changes between consecutive steps, often switching between two or more rules. | Adding X, then subtracting Y; Multiplying by X, then dividing by Y; Subtracting X, then subtracting Y (as in this problem). |
Additional Information: Solving Number Series Questions
Solving number series questions requires careful observation and logical reasoning. Here are some common strategies:
- Calculate the differences between consecutive terms. Look for constant differences, differences that form a new pattern, or alternating differences.
- Calculate the ratios between consecutive terms. This is useful for geometric series or series involving multiplication/division.
- Look for alternating patterns, where the rule changes from one step to the next.
- Consider patterns involving squares, cubes, prime numbers, or other special number sequences.
- Break down complex series into simpler sub-series if possible.
- Practice with various types of series to become familiar with common patterns.
Identifying the pattern is the key step. Once the pattern is found, applying it to find the missing term is usually straightforward.
Important Questions from Number Series
Select the number from among the given options that can replace the question mark (?) in the following series.
37, 52, 74, 104, 143, ?
Select the number that can replace the question mark (?) in the following series.
17, 19, 22, 27, 34, 45, 58,?Select the number from among the given options that can replace the question mark (?) in the following series.
10, 14, 31, 35, 73, 77, ?
Select the number from among the given options that can replace the question mark (?) in the following series.
215, 231, 256, 292, ?
Select the number from among the given options that can replace the question mark (?) in the following series.
6, 6, 8, 24, 28, 140, ?
