A series is given with one term missing. Select the correct alternative from the given ones that will complete the series.
–7
Understanding the Number Series Pattern
The question asks us to find the missing term in the series: 11, 8, 4, –1, ?. To solve this number series problem, we need to identify the pattern or rule that connects consecutive terms.
Analyzing the Differences Between Terms
Let's look at the difference between each term and the one before it:
- Difference between the 2nd and 1st term: $8 - 11 = -3$
- Difference between the 3rd and 2nd term: $4 - 8 = -4$
- Difference between the 4th and 3rd term: $-1 - 4 = -5$
Identifying the Pattern in Differences
We can observe the pattern in the differences we just calculated:
- The first difference is -3.
- The second difference is -4.
- The third difference is -5.
It appears that the difference between consecutive terms is decreasing by 1 each time. The sequence of differences is -3, -4, -5, and so on.
Predicting the Next Difference and Term
Following the pattern of the differences (-3, -4, -5), the next difference should be -6.
To find the next term in the main series, we add this next difference (-6) to the last known term (-1):
Next Term = Last Term + Next Difference
Next Term = $-1 + (-6)$
Next Term = $-1 - 6$
Next Term = $-7$
Conclusion for the Missing Number
Based on the identified pattern where the difference between consecutive terms decreases by 1, the next term in the number series 11, 8, 4, –1, ? is –7.
| Term Number | Term Value | Difference from Previous Term |
|---|---|---|
| 1st | 11 | - |
| 2nd | 8 | $8 - 11 = -3$ |
| 3rd | 4 | $4 - 8 = -4$ |
| 4th | -1 | $-1 - 4 = -5$ |
| 5th | ? | Expected difference: $-6$ |
Calculating the 5th term: $-1 + (-6) = -7$.
Revision Table: Key Concepts in Number Series
| Concept | Description | Example Pattern |
|---|---|---|
| Arithmetic Series | Each term is obtained by adding a constant difference to the previous term. | 2, 5, 8, 11, ... (Difference +3) |
| Geometric Series | Each term is obtained by multiplying the previous term by a constant ratio. | 3, 6, 12, 24, ... (Ratio x2) |
| Difference Series | The differences between consecutive terms form a separate recognizable series (like in this problem). | 1, 2, 4, 7, 11, ... (Differences: +1, +2, +3, +4...) |
| Mixed Series | Involves a combination of patterns or multiple interwoven series. | 1, 5, 2, 6, 3, 7, ... (Interwoven 1,2,3... and 5,6,7...) |
Additional Information on Number Series Reasoning
Number series questions are common in reasoning and aptitude tests. They evaluate your ability to identify patterns and relationships between numbers.
Common patterns to look for include:
- Constant difference (Arithmetic progression).
- Constant ratio (Geometric progression).
- Increasing or decreasing differences (like in this case, an arithmetic progression of differences).
- Increasing or decreasing ratios.
- Alternating patterns.
- Squares, cubes, or other powers of numbers.
- Combinations of operations (e.g., add a number, then multiply by another).
- Fibonacci-like sequences (each term is the sum of the previous two).
Solving number series problems often requires careful observation and testing different potential patterns. Start by calculating differences, ratios, or other simple relationships between terms.
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, ?
