A number series is given with one term missing. Identify the correct number that continues the pattern: 5, 8, 12, 17, 23, ?

Introduction / Context:
This question is an example of a number series where the pattern is hidden in the differences between terms. Detecting such difference based patterns is a core skill in many reasoning and aptitude tests. Here, the numbers are increasing at a gradually changing rate, which signals that the differences themselves follow a simple rule.

Given Data / Assumptions:
We are given the series:
5, 8, 12, 17, 23, ?
We assume that consecutive terms are related by a regular increase that can be identified by examining the gaps between numbers.

Concept / Approach:
The standard approach is to compute the difference between each pair of consecutive terms and see if these differences form an arithmetic sequence or some other simple pattern. Often, for moderately increasing series, the differences themselves increase by 1 or by a fixed amount.

Step-by-Step Solution:
Step 1: Compute the differences.8 - 5 = 312 - 8 = 417 - 12 = 523 - 17 = 6Step 2: Observe the pattern in the differences: 3, 4, 5, 6. These are consecutive integers.Step 3: The next difference should logically be 7 if the pattern continues.Step 4: Add this next difference to the last known term.23 + 7 = 30.

Verification / Alternative check:
We can verify by reconstructing the series using the rule that each new difference is one more than the previous difference. Starting from 5, we add 3 to get 8, add 4 to get 12, add 5 to get 17, add 6 to get 23, and add 7 to reach 30. Everything is consistent and no contradictions occur, so the pattern is reliable.

Why Other Options Are Wrong:
Values like 72, 65, 48, or 27 break the clean difference pattern of 3, 4, 5, 6, 7. For example, if we choose 27, the last difference becomes 4, which repeats a previous gap and destroys the increasing sequence of differences. The other choices distort the series even more severely and therefore cannot be correct.

Common Pitfalls:
A common mistake is to assume a multiplicative pattern when numbers are only growing modestly. Another error is to miscalculate one of the differences, for instance computing 23 - 17 as 5 instead of 6, which leads to an incorrect continuation. Careful subtraction and systematic checking of the difference pattern avoid these issues.

Final Answer:
The correct number that completes the series is 30.