Consider the following number series with alternating operations: 100, 50, 52, 26, 28, ?, 16, 8. Choose the option that correctly replaces the missing term.

Introduction / Context:
This series combines two different operations that alternate as we move from one term to the next. Questions of this type test whether you can detect a repeated cycle of operations, such as halving followed by adding a constant. They are common in reasoning sections of competitive examinations.

Given Data / Assumptions:
The series is:
100, 50, 52, 26, 28, ?, 16, 8
We assume that a consistent two step process is being repeated across the entire series and that we need to identify and apply this cycle to find the missing term in the sixth position.

Concept / Approach:
A quick way to approach such questions is to compare every alternate term. Observe whether there is a pattern of dividing by a fixed number and then adding a constant. Here, the numbers move up and down in a way that suggests halving and then adding a small quantity repeatedly.

Step-by-Step Solution:
Step 1: Compare the first and second terms.100 to 50 is exactly half, so we apply division by 2.Step 2: Compare the second and third terms.50 to 52 is an increase of 2, so we add 2.Step 3: Apply the same pattern again.52 to 26 is a division by 2.26 to 28 is again an increase of 2.Step 4: Continue the established cycle.From 28, the next step in the pattern is division by 2, which gives 28 / 2 = 14.Step 5: Check with the next known term.From 14, we should add 2 to follow the cycle, giving 16, which matches the given term, and from 16, dividing by 2 gives 8, also matching the series.

Verification / Alternative check:
Write the operations explicitly: divide by 2, add 2, divide by 2, add 2, and so on. Applying this cycle from 100 gives 100, 50, 52, 26, 28, 14, 16, 8. Every step respects the same pair of alternating operations, and no inconsistencies appear, which strongly confirms the correctness of the missing term.

Why Other Options Are Wrong:
Values like 30, 32, 38, or 20 do not equal 28 divided by 2 and therefore break the halving step. For example, if we chose 30, then the move from 28 to 30 would be plus 2 rather than division by 2, which would disturb the alternating cycle and make it impossible to reach 16 and 8 correctly using the same pattern.

Common Pitfalls:
Some candidates try to force a single arithmetic progression or a constant difference when the series clearly alternates between two types of operations. Others may miscalculate half of 28 or forget to confirm that the next given term also fits the pattern. Always validate the pattern both forward and backward around the missing term.

Final Answer:
The correct number that should replace the missing term is 14.