In the sequence 4, 8, 14, 22, ?, find the next term.

Introduction / Context:
This is a basic number series question that checks comfort with arithmetic progressions of differences. Instead of a simple arithmetic sequence, the sequence of differences itself forms a simple pattern, which is a very common style in aptitude tests.

Given Data / Assumptions:

• Given sequence: 4, 8, 14, 22, ?
• All terms are integers.
• There is exactly one correct next term which continues the same rule.

Concept / Approach:
When the jump between consecutive terms is not constant, it is natural to look at the differences between the terms. If those differences follow a regular pattern, such as an arithmetic sequence, we can extend the pattern to find the next difference and hence the next term.

Step-by-Step Solution:
Step 1: Compute the differences: 8 − 4 = 4, 14 − 8 = 6, 22 − 14 = 8. Step 2: The differences are 4, 6, and 8. These are consecutive even numbers increasing by 2 each time. Step 3: Following this pattern, the next difference should be 10. Step 4: Add this new difference to the last known term: 22 + 10 = 32.

Verification / Alternative check:
With the candidate term 32, the full series becomes 4, 8, 14, 22, 32. The differences are then 4, 6, 8, 10 which clearly forms an arithmetic progression of even numbers with common difference 2. This confirms that the rule is consistent across all positions, and the value 32 is correct.

Why Other Options Are Wrong:
If we choose 28, the difference from 22 would be 6, and the sequence of differences would be 4, 6, 8, 6 which no longer shows a simple pattern. Similarly, choosing 36 or 46 leads to sequences of differences that do not follow the smooth progression of adding 2 each time. Therefore those values do not preserve the intended rule.

Common Pitfalls:
Students sometimes attempt to guess the next term by estimation instead of checking the exact numerical pattern. Another pitfall is to try multiplication patterns first when the series is actually governed by changing differences. Always compute the first-level differences; it is often the fastest and most reliable approach in such problems.

Final Answer:
The next term that correctly continues the pattern of increasing even differences is 32.