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:

1. 465
2. 428
3. 430
4. 425

Our calculated missing number is 425, which matches option 4.

Revision Table: Number Series Analysis

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.