In the number series 118, 166, 190, 202, 208, ?, identify the next term that correctly follows the observed pattern.

Introduction / Context:
This problem presents a moderately increasing sequence and asks for the next term. The increments between numbers shrink in a regular manner, hinting that the differences between consecutive terms themselves follow a simple rule. Recognising this second level progression is key to solving the question efficiently.

Given Data / Assumptions:

• The series is: 118, 166, 190, 202, 208, ?
• There is exactly one missing term at the end.
• We assume a single, consistent pattern governs the differences.
• No term is intended as an outlier or exception.

Concept / Approach:
The most natural step is to compute the first level differences between consecutive terms and see whether these differences themselves form a simple sequence. Sometimes they may be halved, doubled, or follow an arithmetic progression. Here, the differences appear to be reducing by a factor of 2 each time, suggesting a geometric or halving pattern that can be extended one more step to find the next increment.

Step-by-Step Solution:
Step 1: Compute the differences between consecutive terms. 166 - 118 = 48. 190 - 166 = 24. 202 - 190 = 12. 208 - 202 = 6. Step 2: Observe that each difference is half of the previous one: 48 ÷ 2 = 24, 24 ÷ 2 = 12, 12 ÷ 2 = 6. Step 3: Continue this halving pattern. The next difference should be 6 ÷ 2 = 3. Step 4: Add this difference to the last known term to find the next term: 208 + 3 = 211. Step 5: Thus the missing term is 211.

Verification / Alternative check:
We can reconstruct the series using the rule "add a difference that is half of the previous one." Starting from 118, we add 48 to get 166, add 24 to get 190, add 12 to get 202, add 6 to get 208, and finally add 3 to get 211. Every step follows the same consistent halving pattern, making this a robust explanation of the series.

Why Other Options Are Wrong:
If we selected 222, 233 or 244, the corresponding differences from 208 would be 14, 25 or 36, none of which is half of 6. These numbers introduce a break in the clear halving sequence of increments and therefore cannot be correct. Only 211 preserves the smooth geometric pattern of the differences.

Common Pitfalls:
One pitfall is to attempt to fit a direct polynomial or complex formula for the nth term, which is unnecessary. Another is to assume differences must always be constant, which is not true here. Some learners also stop after noticing the first couple of differences and miss the halving pattern because they do not compute the full set. Carefully listing and examining all differences is essential.

Final Answer:
Following the pattern of halving differences (48, 24, 12, 6, 3), the next term in the series is 211.