Which of the following numbers will replace the question mark (?) in the given series? 25, 15, ?, −5, −15
5
Solving the Number Series Pattern
The question asks us to find the missing number in the given series: 25, 15, ?, −5, −15.
To solve a number series problem, we need to identify the pattern or rule that connects the consecutive terms.
Identifying the Pattern in the Series
Let's look at the differences between the given consecutive terms:
- Difference between the first and second term: $15 - 25 = -10$
- Difference between the fourth and fifth term: $-15 - (-5) = -15 + 5 = -10$
From these calculations, it appears that each term is obtained by subtracting 10 from the previous term. This indicates a consistent difference pattern, characteristic of an arithmetic progression.
Applying the Pattern to Find the Missing Number
Assuming the pattern is subtracting 10 from the previous term, we can find the missing number (?) by applying this rule to the second term (15).
- Second term: 15
- Pattern: Subtract 10
- Missing term = $15 - 10 = 5$
So, the missing number should be 5.
Verifying the Pattern with the Found Number
Let's check if the pattern holds true for the terms after the missing number if we replace '?' with 5.
The series becomes: 25, 15, 5, −5, −15
- Difference between the second and third term: $5 - 15 = -10$
- Difference between the third and fourth term: $-5 - 5 = -10$
The pattern of subtracting 10 is consistent throughout the series when 5 replaces the question mark.
Therefore, the number that replaces the question mark is 5.
Revision Table: Number Series Analysis
| Term Number | Term Value | Difference from Previous Term |
|---|---|---|
| 1 | 25 | - |
| 2 | 15 | $15 - 25 = -10$ |
| 3 | ? (Calculated as 5) | $5 - 15 = -10$ |
| 4 | −5 | $-5 - 5 = -10$ |
| 5 | −15 | $-15 - (-5) = -10$ |
Additional Information: Types of Number Series
Number series problems test your ability to identify patterns. Common patterns include:
- Arithmetic Series: Each term is obtained by adding or subtracting a constant value (called the common difference) from the previous term. The given series is an example of an arithmetic series with a common difference of -10.
- Geometric Series: Each term is obtained by multiplying or dividing the previous term by a constant value (called the common ratio).
- Square or Cube Series: Terms are related to squares or cubes of natural numbers.
- Fibonacci Series: Each term is the sum of the two preceding terms (starting usually from 0 and 1, or 1 and 1).
- Mixed Series: A combination of two or more patterns or alternating patterns.
Understanding these basic types helps in quickly identifying the rule governing a given number series.
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