In the following question, select the missing number from the given series.
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Solving the Missing Number Series: 18, 14, 10, 6, ?
The question asks us to find the missing number in the given series: 18, 14, 10, 6, ?. To solve this missing number series problem, we need to identify the pattern or rule that connects the numbers in the sequence.
Analyzing the Pattern in the Number Series
Let's look at the difference between consecutive terms in the series:
- Difference between the first and second term: \(14 - 18\)
- Difference between the second and third term: \(10 - 14\)
- Difference between the third and fourth term: \(6 - 10\)
Let's calculate these differences:
- \(14 - 18 = -4\)
- \(10 - 14 = -4\)
- \(6 - 10 = -4\)
We can observe a consistent pattern here. Each term is obtained by subtracting 4 from the previous term. This indicates that the series is an arithmetic progression with a common difference of -4.
| Term | Value | Difference from previous term |
|---|---|---|
| 1st | 18 | - |
| 2nd | 14 | \(14 - 18 = -4\) |
| 3rd | 10 | \(10 - 14 = -4\) |
| 4th | 6 | \(6 - 10 = -4\) |
| 5th (Missing Term) | ? | Should be \(6 - 4\) |
Calculating the Missing Number
Following the identified pattern, the next number in the series will be obtained by subtracting 4 from the last given term, which is 6.
Missing number \(= 6 - 4\)
Missing number \(= 2\)
So, the missing number in the series 18, 14, 10, 6, ? is 2.
Step-by-Step Solution
- Examine the given number series: 18, 14, 10, 6, ?.
- Find the difference between consecutive numbers: \(14-18 = -4\), \(10-14 = -4\), \(6-10 = -4\).
- Identify the pattern: The pattern is subtracting 4 from each term to get the next term.
- Apply the pattern to the last given number (6) to find the missing number.
- Calculate \(6 - 4\).
- The result, 2, is the missing number in the series.
Revision Table: Number Series Pattern
| Series Type | Common Pattern | Example |
|---|---|---|
| Arithmetic Series | Adding or Subtracting a constant value (common difference) | 2, 5, 8, 11... (add 3) 18, 14, 10, 6... (subtract 4) |
| Geometric Series | Multiplying or Dividing by a constant value (common ratio) | 2, 6, 18, 54... (multiply by 3) 64, 32, 16, 8... (divide by 2) |
| Difference Series | Differences between terms follow a pattern (e.g., arithmetic, prime numbers, squares) | 1, 3, 7, 13, 21... (differences are 2, 4, 6, 8...) |
Additional Information: Solving Number Series Questions
Solving number series questions is a common part of logical reasoning tests. Here are some tips for finding the missing number:
- Look for common differences or ratios between consecutive terms.
- Check for patterns in the differences or ratios themselves.
- Consider squares, cubes, prime numbers, or Fibonacci sequence.
- Look for alternating patterns (e.g., add 2, then subtract 1, then add 2, etc.).
- Sometimes, the pattern might involve operations on two previous terms to get the next term.
- Practice with various types of series to improve pattern recognition skills.
Similar Questions
- Choose the missing number in the below series.
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Important Questions from Number Series
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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, .........
