In the following number series question from verbal reasoning, one term is missing. Observe the sequence 9, 13, 18, 24, 31, ? and choose the correct alternative that completes the series.

Introduction / Context:
This question tests the ability to identify a simple pattern in a number series. The given sequence is 9, 13, 18, 24, 31, ?, and we need to determine the missing next term. Recognising patterns in incremental differences is a core skill in verbal reasoning and quantitative aptitude sections of many exams.

Given Data / Assumptions:
Series: 9, 13, 18, 24, 31, ?
Exactly one term is missing at the end of the series.
The same rule should apply consistently between every pair of consecutive terms.
Only one of the provided options should fit the discovered pattern.

Concept / Approach:
The most natural way to tackle this series is to examine the differences between consecutive terms. If the differences themselves follow a clear pattern, we can extrapolate them. For many exam questions, differences increase or decrease regularly by 1, 2, or some small integer. We therefore compute each difference and see whether they form a familiar sequence such as consecutive integers.

Step-by-Step Solution:
Difference between 9 and 13: 13 - 9 = 4. Difference between 13 and 18: 18 - 13 = 5. Difference between 18 and 24: 24 - 18 = 6. Difference between 24 and 31: 31 - 24 = 7. The differences are 4, 5, 6, 7, which are consecutive integers. Next difference should be 8, so the missing term is 31 + 8 = 39. Therefore, the required number is 39.

Verification / Alternative check:
Checking the reconstructed sequence: 9, 13, 18, 24, 31, 39. The differences are 4, 5, 6, 7, 8, which form a smooth increasing sequence. None of the other options would create such a neat pattern of consecutive differences. This confirms that 39 is the only value that continues the logic in a consistent manner.

Why Other Options Are Wrong:
Option B: 35 gives a final difference of 4 (31 to 35), which breaks the increasing trend of 4, 5, 6, 7.
Option C: 40 gives a difference of 9, jumping too far ahead and skipping 8 in the difference sequence.
Option D: 37 gives a difference of 6, repeating an earlier difference instead of continuing the pattern.
Option E: 45 produces a difference of 14, which is completely inconsistent with the smooth progression of small integers.

Common Pitfalls:
A frequent mistake is to look for multiplicative patterns where only simple addition is needed. Some students also overlook the idea that differences themselves can form a separate sequence with its own regularity. In competitive exams, many number series rely exactly on this principle: differences or second-level differences behave in a simple and predictable way.

Final Answer:
The number that correctly completes the series is 39, so the correct option is 39.