In the number series 54, 51, 48, 45, 42, ?, one term is missing. Choose the correct number that should come next in the sequence.

Introduction / Context:
This problem presents a simple decreasing number series where the terms appear to fall at a steady pace. Many exam questions use such sequences to quickly test whether a candidate can recognize a constant difference between consecutive numbers and extend the pattern accordingly.

Given Data / Assumptions:
The series is:
54, 51, 48, 45, 42, ?
We assume that the pattern is governed by a constant subtraction at each step, and our task is to identify that constant and apply it to find the next term.

Concept / Approach:
The key idea is to calculate the difference between each pair of consecutive terms and check whether this difference stays the same throughout the series. When all differences are identical, the series is a simple arithmetic progression, and extending it becomes straightforward.

Step-by-Step Solution:
Step 1: Compute the consecutive differences.51 - 54 = -348 - 51 = -345 - 48 = -342 - 45 = -3Step 2: Observe that each term is 3 less than the previous term, so the constant difference is -3.Step 3: Apply this difference to the last known term.42 - 3 = 39.

Verification / Alternative check:
We can reconstruct the series from the first term using the rule that each next term equals the previous term minus 3. Starting from 54, we get 51, 48, 45, 42, and then 39. The pattern remains perfectly consistent, confirming that subtraction of 3 at each step is indeed the governing rule of the sequence.

Why Other Options Are Wrong:
Values such as 38, 36, 40, or 41 do not fit the rule of subtracting 3 each time. For example, 38 would represent a difference of -4 from 42, while 40 would represent a difference of -2, both of which break the uniform step size. Only 39 maintains the constant decrease of 3 that characterizes the entire series.

Common Pitfalls:
Sometimes test takers miscalculate one of the differences, especially when working quickly, and then infer a wrong rule. Another mistake is to overcomplicate a clearly simple pattern by looking for multiplicative or alternating operations when none are needed. Always check for a constant difference first in regularly spaced sequences.

Final Answer:
The next number in the series that maintains the pattern is 39.