In the following question, select the missing number from the given series, which decreases by a constant amount each time. 672, 666, 660, 654, ?

Introduction / Context:
This number series decreases steadily by the same amount at each step. The learner must recognise this constant difference and apply it to find the next term. Such linear decreasing sequences are foundational in number series practice.

Given Data / Assumptions:
- Series: 672, 666, 660, 654, ? - The fifth term is missing. - The series appears to be descending by equal steps.

Concept / Approach:
To identify a constant difference, compute the subtraction between each pair of consecutive terms. If the difference is the same, the series is an arithmetic progression with a negative common difference. The missing term is found by subtracting this difference from the last known value.

Step-by-Step Solution:
Step 1: Compute differences. 666 - 672 = -6. 660 - 666 = -6. 654 - 660 = -6. Step 2: The common difference is -6 at each step. Step 3: To find the next term, subtract 6 from 654. Step 4: 654 - 6 = 648.

Verification / Alternative check:
Rebuild the series starting from 672 and repeatedly subtract 6: 672, 666, 660, 654, 648. This matches the pattern of equal decrements and confirms that 648 is the correct missing term.

Why Other Options Are Wrong:
- Option 650 would imply a difference of -4 from 654, which breaks the constant step of -6. - Option 646 would require a difference of -8, again inconsistent with the pattern. - Option 652 gives a difference of -2, which also does not match the regular change.

Common Pitfalls:
Learners sometimes miscalculate one subtraction and then assume a different pattern. Others may try to overcomplicate a simple linear series. Always start with basic first differences before considering more complex structures.

Final Answer:
The missing term in the series is 648, so the correct option is 648.