In the following question, select the missing number from the given series. 600, 565, 530, 495, 460, ?
425
Finding the Missing Number in a Numerical Series
The question asks us to identify the missing number in the given series: 600, 565, 530, 495, 460, ?
To find the missing number, we need to determine the pattern or rule that governs the series. Let's look at the difference between consecutive terms.
Analyzing the Series Pattern
We calculate the difference between each term and the term immediately following it:
- Difference between the first and second term: $565 - 600 = -35$
- Difference between the second and third term: $530 - 565 = -35$
- Difference between the third and fourth term: $495 - 530 = -35$
- Difference between the fourth and fifth term: $460 - 495 = -35$
The difference between consecutive terms is consistently -35. This indicates that the series is an arithmetic progression where each subsequent term is obtained by subtracting 35 from the previous term. The common difference is -35.
Calculating the Missing Term
To find the missing number, which is the term after 460, we need to apply the same pattern. We subtract the common difference (-35) from the last known term (460).
Missing number = $460 - 35$
Missing number = $425$
Therefore, the missing number in the series is 425.
Identifying the Correct Option
Let's check the given options:
- 465
- 428
- 430
- 425
Our calculated missing number is 425, which matches option 4.
| Term | Value | Difference from previous term |
|---|---|---|
| 1st | 600 | - |
| 2nd | 565 | $565 - 600 = -35$ |
| 3rd | 530 | $530 - 565 = -35$ |
| 4th | 495 | $495 - 530 = -35$ |
| 5th | 460 | $460 - 495 = -35$ |
| 6th (Missing) | 425 | $425 - 460 = -35$ |
Revision Table: Number Series Analysis
| Concept | Description |
|---|---|
| Number Series | A sequence of numbers following a specific pattern or rule. |
| Arithmetic Series | A series where the difference between consecutive terms is constant (common difference). |
| Common Difference | The constant value added to each term to get the next term in an arithmetic series. Here, it's -35. |
Additional Information: Understanding Arithmetic Progression
An arithmetic progression (AP) is a sequence of numbers such that the difference between the consecutive terms is constant. This constant difference is called the common difference, denoted by 'd'.
The general form of an arithmetic progression is:
$a, a+d, a+2d, a+3d, \dots, a+(n-1)d$
where:
- 'a' is the first term
- 'd' is the common difference
- 'n' is the term number
In the given series 600, 565, 530, 495, 460, ...
- The first term $a = 600$.
- The common difference $d = -35$.
The series terms are generated as follows:
- 1st term: $a = 600$
- 2nd term: $a + d = 600 + (-35) = 565$
- 3rd term: $a + 2d = 600 + 2(-35) = 600 - 70 = 530$
- 4th term: $a + 3d = 600 + 3(-35) = 600 - 105 = 495$
- 5th term: $a + 4d = 600 + 4(-35) = 600 - 140 = 460$
- 6th term: $a + 5d = 600 + 5(-35) = 600 - 175 = 425$
This confirms our calculation that the missing number is 425.
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