In the following question, select the missing number from the given series.
30
Solving Number Series Questions: Finding the Missing Term
This question asks us to find the missing number in the given series: 5, 8, 12, 17, 23, ?
To solve number series problems, we need to identify the pattern or rule that connects the terms. Let's look at the differences between consecutive terms in this series.
Step-by-Step Analysis of the Series Pattern
Let's calculate the difference between each term and the one before it:
- Difference between the 2nd term (8) and the 1st term (5): \(8 - 5 = 3\)
- Difference between the 3rd term (12) and the 2nd term (8): \(12 - 8 = 4\)
- Difference between the 4th term (17) and the 3rd term (12): \(17 - 12 = 5\)
- Difference between the 5th term (23) and the 4th term (17): \(23 - 17 = 6\)
We can observe a clear pattern in the differences:
| Terms | Difference |
|---|---|
| 8 - 5 | 3 |
| 12 - 8 | 4 |
| 17 - 12 | 5 |
| 23 - 17 | 6 |
The differences between consecutive terms are increasing by 1 each time (3, 4, 5, 6). This means the next difference in the series should be 7.
Calculating the Missing Number
Following the identified pattern, the next number in the series will be obtained by adding the next difference (which is 7) to the last term (23).
Missing Number = Last Term + Next Difference
Missing Number = \(23 + 7\)
Missing Number = \(30\)
Therefore, the missing number in the series 5, 8, 12, 17, 23, ? is 30.
The complete series is 5, 8, 12, 17, 23, 30.
Verifying the Options
Let's check our calculated missing number against the given options:
- Option 1: 28 (Does not match 30)
- Option 2: 30 (Matches 30)
- Option 3: 31 (Does not match 30)
- Option 4: 29 (Does not match 30)
Our calculated missing number, 30, matches Option 2.
Revision Table: Key Concepts for Number Series
| Concept | Description | Example Pattern Type |
|---|---|---|
| Difference Series | Finding the pattern in the differences between consecutive terms. | Arithmetic progression of differences (as in this question). |
| Ratio Series | Finding the pattern in the ratio between consecutive terms (multiplication/division). | Geometric progression (e.g., 2, 4, 8, 16...). |
| Mixed Series | A combination of different patterns (e.g., addition followed by multiplication, or two interleaved series). | Series involving squares, cubes, primes, etc. |
| Step Method | Analyzing differences of differences (second-order differences, third-order, etc.). | Useful when the first-order difference series doesn't have a simple pattern. |
Additional Information on Number Series Problems
Number series problems are common in various aptitude tests. They assess your ability to identify logical rules and patterns. Here are some tips for approaching them:
- Always start by calculating the differences between consecutive terms. This is the most common type of pattern.
- If the differences don't show a simple pattern, look at the ratios between terms (for multiplication/division series).
- Consider second-order differences (the differences between the differences).
- Look for patterns involving squares, cubes, prime numbers, Fibonacci sequence, or alternating patterns.
- Sometimes, two independent series are interleaved.
- Practice with various types of series to become familiar with different patterns.
Understanding these basic techniques will help you solve a wide range of number series questions like the one involving 5, 8, 12, 17, 23, ?.
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