Which of the following numbers will replace the question mark (?) in the given series? 54, 46, 34, 26, 14, ?
6
Analyzing the Given Number Series
We are given a number series: 54, 46, 34, 26, 14, ?. Our goal is to find the pattern in this series and determine the number that should replace the question mark. Number series questions are common in aptitude tests and require identifying the relationship between consecutive terms.
Finding the Difference Pattern
A common method to find the pattern in a number series is to look at the difference between consecutive terms. Let's calculate the differences:
- Difference between the 2nd and 1st term: 46 - 54
- Difference between the 3rd and 2nd term: 34 - 46
- Difference between the 4th and 3rd term: 26 - 34
- Difference between the 5th and 4th term: 14 - 26
- Difference between the ? and 5th term: ? - 14
Let's calculate these differences:
- $\text{Difference}_1 = 46 - 54 = -8$
- $\text{Difference}_2 = 34 - 46 = -12$
- $\text{Difference}_3 = 26 - 34 = -8$
- $\text{Difference}_4 = 14 - 26 = -12$
| Terms | Difference |
|---|---|
| 54, 46 | -8 |
| 46, 34 | -12 |
| 34, 26 | -8 |
| 26, 14 | -12 |
Identifying the Series Pattern
Looking at the calculated differences (-8, -12, -8, -12), we can see a repeating pattern. The difference alternates between -8 and -12. The pattern of differences is -8, -12, -8, -12, and so on.
Determining the Next Number
Following the identified pattern, the next difference in the series should be -8 (since the last difference was -12). To find the next number in the series, we need to subtract this difference from the last known term, which is 14.
Next number = Last term + Next difference
Next number = $14 + (-8)$
Next number = $14 - 8$
Next number = $6$
Therefore, the number that replaces the question mark (?) in the given series is 6.
Revision Table: Number Series Analysis
| Term Position | Number | Difference from previous term |
|---|---|---|
| 1st | 54 | - |
| 2nd | 46 | $46 - 54 = -8$ |
| 3rd | 34 | $34 - 46 = -12$ |
| 4th | 26 | $26 - 34 = -8$ |
| 5th | 14 | $14 - 26 = -12$ |
| 6th | ? (6) | $6 - 14 = -8$ |
Additional Information: Types of Number Series
Number series problems can involve various types of patterns. Some common types include:
- Arithmetic Series: Each term is obtained by adding a constant value (common difference) to the previous term.
- Geometric Series: Each term is obtained by multiplying the previous term by a constant value (common ratio).
- Difference Series: The pattern is found in the differences between consecutive terms, as seen in the example above. The differences themselves might form an arithmetic or geometric series, or follow another pattern like alternating values.
- Mixed Series: Series that combine two or more different patterns.
- Fibonacci Series: Each term is the sum of the two preceding terms (e.g., 0, 1, 1, 2, 3, 5, 8...).
- Square or Cube Series: Terms are squares, cubes, or related to squares/cubes of natural numbers.
To solve number series questions, it's helpful to try calculating differences, ratios, or look for relationships involving squares, cubes, or other mathematical operations.
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, ?
