Understanding the Number Series Pattern

We are given a number series: 15, 20, 18, 23, ?, 26, 24. Our goal is to find the number that is missing from this series.

To find the missing number in a series, we need to identify the rule or pattern that connects the numbers in the sequence. Let's look at the differences or relationships between consecutive terms.

Identifying the Number Series Pattern

Let's examine the transitions between the given numbers:

• From the 1st term (15) to the 2nd term (20): $20 - 15 = 5$ (Increase of 5)
• From the 2nd term (20) to the 3rd term (18): $18 - 20 = -2$ (Decrease of 2)
• From the 3rd term (18) to the 4th term (23): $23 - 18 = 5$ (Increase of 5)
• From the 4th term (23) to the missing term (?): Let's assume the pattern continues.
• From the term after the missing term (26) to the last term (24): $24 - 26 = -2$ (Decrease of 2)

Observing the differences, we see a repeating pattern of operations:

\(+5, -2, +5, ?, ?, -2\)

The pattern appears to be an alternation of adding 5 and subtracting 2.

Calculating the Missing Number

Following the identified pattern (+5, -2, +5, ...):

• The step from 15 to 20 is +5.
• The step from 20 to 18 is -2.
• The step from 18 to 23 is +5.
• The next step should be -2 from 23 to find the missing number.

So, the missing number is calculated as:

\(23 - 2 = 21\)

Verifying the Pattern

If the missing number is 21, let's check if the pattern holds for the remaining terms:

• From 23 to 21 (the missing number): This step was calculated as -2, following the pattern.
• From 21 to 26: The pattern dictates the next step should be +5. \(21 + 5 = 26\). This matches the number provided after the missing term.
• From 26 to 24: The pattern dictates the next step should be -2. \(26 - 2 = 24\). This matches the last number in the series.

The pattern (+5, -2) is consistent throughout the entire series when the missing number is 21.

Conclusion on the Missing Number

Based on the consistent pattern of alternating +5 and -2, the missing number in the series 15, 20, 18, 23, ?, 26, 24 is 21.

Revision Table for Number Series

Additional Information on Number Series Questions

Number series problems are common in aptitude tests. They test your ability to identify mathematical patterns. Some common types of patterns include:

• Arithmetic progression (constant difference)
• Geometric progression (constant ratio)
• Alternating series (different operations/patterns applied alternately)
• Fibonacci series (each number is the sum of the two preceding ones)
• Series based on squares, cubes, or other powers
• Combination of multiple patterns

Solving these problems often involves looking at differences between consecutive terms, ratios, or relationships between alternate terms. Sometimes, splitting the series into two separate alternating series can reveal the pattern.