Finding the Missing Number in the Series

The question asks us to find the missing number in the given series: 14, 18, 21, 25, 28, ?

Let's analyze the pattern between consecutive terms in the series.

• Difference between the second term (18) and the first term (14): \(18 - 14 = 4\)
• Difference between the third term (21) and the second term (18): \(21 - 18 = 3\)
• Difference between the fourth term (25) and the third term (21): \(25 - 21 = 4\)
• Difference between the fifth term (28) and the fourth term (25): \(28 - 25 = 3\)

Observing the differences, we can see an alternating pattern of adding 4 and then adding 3 to the previous term:

• \(14 + 4 = 18\)
• \(18 + 3 = 21\)
• \(21 + 4 = 25\)
• \(25 + 3 = 28\)

Following this alternating pattern, the next step after adding 3 should be adding 4 to the last known term (28).

So, the missing number will be:

\(28 + 4 = 32\)

Therefore, the missing number in the series is 32.

Verifying the Options

Let's look at the given options:

1. 32
2. 31
3. 30
4. 35

Our calculated missing number is 32, which matches option 1.

Step-by-Step Solution

1. Examine the differences between consecutive numbers in the series.
2. Identify the pattern of the differences: +4, +3, +4, +3, ...
3. Apply the next step in the pattern to the last number in the series.
4. The last number is 28, and the next operation in the pattern is +4.
5. Calculate \(28 + 4 = 32\).
6. The missing number is 32.

The series with the missing number is 14, 18, 21, 25, 28, 32.

Revision Table: Number Series Patterns

Additional Information: Solving Number Series Questions

Solving number series questions involves identifying the underlying rule or pattern that connects the terms. Common patterns include:

• Adding or subtracting a constant number.
• Multiplying or dividing by a constant number.
• Alternating addition/subtraction or multiplication/division.
• Adding/subtracting numbers that form their own series (e.g., arithmetic or geometric progression).
• Squares or cubes of numbers, or related to them (e.g., \(n^2\), \(n^2 \pm 1\), \(n^3\), \(n^3 \pm 1\)).
• Fibonacci sequence or similar recursive patterns where a term depends on previous terms.

To solve these problems effectively:

• Calculate the differences or ratios between consecutive terms.
• Look for patterns in these differences or ratios.
• If the first level of differences doesn't show a clear pattern, calculate the differences of the differences (second-level differences).
• Consider other relationships like squares, cubes, or alternating operations.
• Test the identified pattern against all given terms to ensure it holds true.