In the following question, select the missing number from the given decreasing series: 146, 137, 128, ?, 110, 101.

Introduction / Context:
This question presents a simple decreasing number series where each term is obtained by subtracting a constant amount from the previous term. The aim is to identify that constant difference and use it to find the missing value. Such uniform decrement series are among the most basic patterns in number series questions and are often used to check quick observation skills.

Given Data / Assumptions:

• Series: 146, 137, 128, ?, 110, 101.
• One middle term is missing.
• The sequence appears to be decreasing steadily by a fixed number.

Concept / Approach:
For a series that appears to decline smoothly, the natural first step is to compute the difference between easily visible consecutive terms. If that difference is constant, the entire sequence is likely an arithmetic progression. In this case, we can then insert the missing term by subtracting the same constant difference for each step, both before and after the blank.

Step-by-Step Solution:
Step 1: Calculate the difference between the first and second terms. 137 - 146 = -9, so the series goes down by 9 from 146 to 137. Step 2: Calculate the difference between the second and third terms. 128 - 137 = -9, again a decrease of 9. Step 3: Check a later visible step to see if the same difference holds. 110 - 119 would be -9, and 101 - 110 = -9, so it is reasonable to assume that each step is a decrease by 9. Step 4: To find the missing term, subtract 9 from 128. 128 - 9 = 119, so the blank should be 119.

Verification / Alternative check:
Write the completed sequence with the missing term filled in: 146, 137, 128, 119, 110, 101. Now check every difference: 137 - 146 = -9, 128 - 137 = -9, 119 - 128 = -9, 110 - 119 = -9, and 101 - 110 = -9. The constant difference of -9 is maintained across the entire series, confirming that 119 is completely consistent with the pattern.

Why Other Options Are Wrong:
If we choose 123, 121, or 117, at least one of the differences between consecutive terms will not equal -9. For example, if the missing term were 121, then 128 - 137 = -9 but 121 - 128 = -7, breaking the uniform step size. Since the question clearly follows a constant decrement rule, any option that produces a different difference is incorrect.

Common Pitfalls:
Students sometimes overcomplicate simple series by looking for multiplicative or mixed operations when a constant addition or subtraction is enough. Another mistake is to compute only a single difference and assume a pattern without verifying it across the whole sequence. Always validate a suspected constant difference at multiple points before finalising your answer.

Final Answer:
The missing number in the series is 119.