Understanding the Number Series Question

The question asks us to identify the missing number in the given series: 3, 8, 13, 18, ?. This is a common type of logical reasoning problem where we need to find the pattern in the sequence of numbers.

Analyzing the Pattern in the Series

Let's look at the difference between consecutive terms in the given series:

• Difference between the 2nd term (8) and the 1st term (3): \(8 - 3 = 5\)
• Difference between the 3rd term (13) and the 2nd term (8): \(13 - 8 = 5\)
• Difference between the 4th term (18) and the 3rd term (13): \(18 - 13 = 5\)

We can clearly see a consistent pattern here. Each term is obtained by adding 5 to the previous term. This means the series is an arithmetic progression with a common difference of 5.

Calculating the Missing Number

To find the missing number, which is the 5th term in the series, we need to apply the same pattern. We add the common difference (5) to the 4th term (18).

Missing Number = 4th term + Common difference

Missing Number = \(18 + 5\)

Missing Number = \(23\)

Therefore, the missing number in the series 3, 8, 13, 18, ? is 23.

Conclusion for the Missing Number

Based on the analysis of the pattern where each successive number is 5 more than the previous one, the next number in the series 3, 8, 13, 18, ? is 23.

Revision Table: Number Series Concepts

Additional Information: Solving Number Series Problems

Solving number series problems often involves identifying the underlying rule or pattern. Here are some common types of patterns you might encounter:

• Arithmetic Series: Constant difference between terms.
• Geometric Series: Constant ratio between terms.
• Mixed Series: Combination of two or more series.
• Difference Series: Pattern found by looking at the differences, or differences of differences, etc.
• Square/Cube Series: Terms related to squares or cubes of natural numbers.
• Prime Number Series: Sequence involves prime numbers.
• Fibonacci Series: Each term is the sum of the two preceding ones (e.g., 0, 1, 1, 2, 3, 5...).

To solve these problems, always start by calculating the differences or ratios between consecutive terms. This is often the simplest way to reveal the pattern, as demonstrated in the solution to the current problem.