Solving the Missing Number Series

This question asks us to find the missing number in the given series: 67, 46, 24, 1, –23, ?. To solve this, we need to identify the pattern or rule that connects the consecutive terms in the series. Number series questions often involve arithmetic progressions, geometric progressions, or patterns based on differences or ratios between terms.

Identifying the Pattern in the Number Series

Let's examine the difference between consecutive terms in the series. Subtracting the second term from the first, the third from the second, and so on, can help reveal an arithmetic pattern if one exists.

• Difference between the 1st and 2nd term: \(46 - 67\)
• Difference between the 2nd and 3rd term: \(24 - 46\)
• Difference between the 3rd and 4th term: \(1 - 24\)
• Difference between the 4th and 5th term: \(-23 - 1\)
• Difference between the 5th and 6th term: \(? - (-23)\)

Calculating the Differences

Let's calculate these differences step-by-step:

Analyzing the Differences Pattern

Looking at the calculated differences (–21, –22, –23, –24), we can observe a clear pattern. The difference between consecutive terms is decreasing by 1 each time. This suggests that the next difference in the series should follow this pattern.

Determining the Next Difference and the Missing Number

Based on the pattern of differences (–21, –22, –23, –24), the next difference should be –25.

To find the missing number, we need to subtract this next difference (–25) from the last given term, which is –23.

Missing Number = Last Term + Next Difference

Missing Number = \(-23 + (-25)\)

Missing Number = \(-23 - 25\)

Missing Number = \(-48\)

So, the missing number in the series is –48.

Conclusion

The series follows a pattern where the difference between consecutive terms decreases by 1 each time. By identifying this pattern, we found the missing number to be –48. The completed series is 67, 46, 24, 1, –23, –48.

Revision Table: Number Series Analysis

Additional Information: Types of Number Series Patterns

Number series questions are common in aptitude tests. Recognizing different types of patterns is key to solving them quickly. Some common patterns include:

• Arithmetic Series: A constant difference between terms (e.g., 2, 5, 8, 11...).
• Geometric Series: A constant ratio between terms (e.g., 3, 6, 12, 24...).
• Difference Series: The difference between consecutive terms follows a pattern itself, as seen in this question (e.g., differences forming an arithmetic series).
• Mixed Series: Combining two or more simple series.
• Fibonacci Series: Each term is the sum of the two preceding ones (e.g., 0, 1, 1, 2, 3, 5...).
• Square/Cube Series: Terms based on squares or cubes of numbers (e.g., 1, 4, 9, 16...).

Practice helps in quickly identifying the type of pattern and applying the correct logic to find the missing or next term.