In the series 8, 14, 24, 40, ?, find the next term that correctly continues the numeric pattern.

Introduction / Context:
This is a number series completion problem where the next term must be deduced from the pattern formed by the given numbers. The series does not grow by a constant difference, so we examine how the differences themselves change from one step to the next.

Given Data / Assumptions:

• Series: 8, 14, 24, 40, ?
• All numbers are positive integers.
• We assume a single consistent rule that generates each term from its predecessors.

Concept / Approach:
The usual strategy when the differences are not constant is to compute first level differences and then second level differences. If the second level differences show a simple pattern, we treat the series as a second order arithmetic progression, which is quite common in exam questions.

Step-by-Step Solution:
Step 1: Compute first differences: 14 - 8 = 6, 24 - 14 = 10, 40 - 24 = 16.Step 2: The first differences are 6, 10 and 16, which are not constant.Step 3: Compute second differences: 10 - 6 = 4 and 16 - 10 = 6. We see the second differences increasing.Step 4: The increase from 4 to 6 suggests the next second difference will be 8, following a pattern that grows by 2 each time.Step 5: The next first difference is therefore 16 + 8 = 24.Step 6: Add this to the last term: 40 + 24 = 64.

Verification / Alternative check:
We can view the first differences directly as 6, 10, 16, 24. The increases between them are 4, 6 and then logically 8. These are themselves simple even numbers increasing by 2. Since this structure is smooth and natural, 64 is strongly supported as the next term. No other candidate maintains this precise second difference pattern.

Why Other Options Are Wrong:
Values such as 52, 56, 72 or 80 give rise to first or second differences that do not follow a simple numeric structure. They produce jumps that break the increasing even second differences pattern of 4, 6, 8 and so on. Only 64 keeps the differences in a clean numeric progression.

Common Pitfalls:
Learners sometimes stop after checking only first differences and assume there is no pattern. Many exam series are designed as second order progressions, where second differences form the regular pattern. It is also a mistake to guess based only on rough growth without calculating differences.

Final Answer:
The next term that correctly continues the series is 64.