In the number series 4, 8, 15, 25, 36, 54, one term is incorrect. Which number from the options should replace the wrong term so that the series follows a consistent pattern?

Introduction / Context:
This question does not ask for the next term but instead asks for a correction to one of the existing terms. One term in the middle of the series is wrong, and we must decide which replacement value from the options produces a consistent numeric pattern throughout the series.

Given Data / Assumptions:

• Original series: 4, 8, 15, 25, 36, 54.
• Exactly one term is incorrect.
• We must replace the wrong term with one of the given alternatives to create a regular pattern.

Concept / Approach:
The strategy is to look for a simple rule that links the first few terms and then see where that rule fails. Often such series are based on increasing differences that themselves follow a simple arithmetic sequence. Once we identify the intended rule, we can determine what number should occupy the incorrect position.

Step-by-Step Solution:
Step 1: Consider the given terms: 4, 8, 15, 25, 36, 54 and compute differences: 8 - 4 = 4, 15 - 8 = 7, 25 - 15 = 10, 36 - 25 = 11, 54 - 36 = 18.Step 2: The differences 4, 7, 10 suggest an intended pattern where each difference increases by 3: 4, 7, 10, 13, 16 and so on.Step 3: If we continue this pattern, after 25 the next difference should be 13, so the next term should be 25 + 13 = 38, not 36.Step 4: Continuing further, the next difference should be 16, giving 38 + 16 = 54, which matches the last term.Step 5: This shows that the correct series is 4, 8, 15, 25, 38, 54, and 36 is the wrong term.Step 6: Therefore the number that should replace the wrong term is 38.

Verification / Alternative check:
If we adopt 38 as the replacement, the full difference pattern becomes 4, 7, 10, 13, 16, which increases regularly by 3. Trying any other suggested replacement, such as 28, 30, 40 or 48, fails to produce this smooth increment pattern and leads to irregular jumps.

Why Other Options Are Wrong:
Replacing 36 with 28, 30, 40 or 48 results in difference sequences that are inconsistent and lack a simple formal rule. None of these choices create a steady increase of 3 in the differences, so they cannot represent the intended series.

Common Pitfalls:
One pitfall is to treat the last term as suspicious because it is largest, rather than carefully examining the difference pattern. Another error is to look only at a part of the series and overlook that the later terms can confirm or refute a hypothesised rule.

Final Answer:
The number that should replace the incorrect term in the series is 38.