Finding the Missing Number in a Number Series

The question asks us to find the number that should replace the question mark (?) in the given number series: 512, 508, 500, 496, ?, 484.

To solve this type of problem, we need to identify the pattern or rule governing the sequence of numbers. Let's look at the difference between consecutive terms in the series.

Analyzing the Pattern in the Number Series

Let's calculate the difference between adjacent numbers:

• Difference between the 1st and 2nd term: $512 - 508 = 4$
• Difference between the 2nd and 3rd term: $508 - 500 = 8$
• Difference between the 3rd and 4th term: $500 - 496 = 4$

We can see a repeating pattern in the differences: the first difference is 4, the second is 8, and the third is 4 again. This suggests the pattern of subtraction is alternating between subtracting 4 and subtracting 8.

The sequence of subtractions seems to be $-4, -8, -4, -8, -4, ...$

Applying the Pattern to Find the Missing Number

Following the identified pattern:

1. The first step is $512 - 4 = 508$.
2. The second step is $508 - 8 = 500$.
3. The third step is $500 - 4 = 496$.
4. The fourth step should be subtracting 8 from the 4th term to get the missing number.

So, the missing number is $496 - 8$.

Calculation: $496 - 8 = 488$.

Let's verify if the pattern continues correctly with the next number provided (484).

If the missing number is 488, the next step in the pattern should be subtracting 4 (since the previous step was subtracting 8). Let's check the difference between 488 and the last number, 484.

Difference between 488 and 484: $488 - 484 = 4$.

This matches the pattern of alternating subtractions: $-4, -8, -4, -8, -4$. The sequence of differences is 4, 8, 4, 8, 4. This means the operations are $-4$, $-8$, $-4$, $-8$, $-4$.

The series with the missing number filled in is: 512, 508, 500, 496, 488, 484.

The pattern of subtracting 4 and then subtracting 8 alternately fits the given series perfectly.

Conclusion on the Missing Number

Based on the identified pattern, the number that replaces the question mark (?) is 488.

Revision Table: Number Series Pattern

Additional Information on Number Series

Number series questions are common in reasoning tests. They assess your ability to identify patterns in sequences of numbers. Patterns can involve various mathematical operations, such as addition, subtraction, multiplication, division, squares, cubes, or a combination of these, sometimes in an alternating or increasing/decreasing manner.

Common types of number series patterns include:

• Arithmetic Series: A constant difference between consecutive terms.
• Geometric Series: A constant ratio between consecutive terms.
• Difference Series: The difference between consecutive terms follows a pattern itself (like in this problem).
• Alternating Series: The pattern alternates between two different rules or operations.
• Fibonacci Series: Each term is the sum of the two preceding terms.
• Square/Cube Series: Terms are squares or cubes of natural numbers, or derived from them.

Solving number series problems often requires trial and error, trying different basic operations and looking for consistency in the differences, ratios, or other relationships between terms.