What should come in place of the question mark (?) in the following number series, where the pattern is based on changing differences? 1, 244, 163, 190, 181, ?,

Introduction / Context:
This series involves terms that do not follow a simple linear rule but instead use differences that themselves form a geometric pattern. The learner must compute the differences between terms, recognise the structure of those differences, and then extend this structure to find the missing term.

Given Data / Assumptions:
- Series: 1, 244, 163, 190, 181, ? - The sixth term is missing. - The differences between consecutive terms are not constant but appear to follow a pattern.

Concept / Approach:
First, calculate the difference between each pair of consecutive terms. Then, examine these differences to see whether they follow a recognisable pattern. In this case, the differences form a geometric progression with a negative ratio. Once that pattern is clear, the next difference can be predicted, and the missing term in the original series can be computed.

Step-by-Step Solution:
Step 1: Compute differences. 244 - 1 = 243. 163 - 244 = -81. 190 - 163 = 27. 181 - 190 = -9. Step 2: The sequence of differences is 243, -81, 27, -9. Step 3: Observe that each difference is obtained by multiplying the previous difference by -1 / 3. Step 4: To find the next difference, multiply -9 by -1 / 3, which gives 3. Step 5: Add this next difference to the last known term: 181 + 3 = 184.

Verification / Alternative check:
Check the ratio between consecutive differences. -81 ÷ 243 = -1 / 3, 27 ÷ -81 = -1 / 3, and -9 ÷ 27 = -1 / 3. This confirms the geometric pattern with ratio -1 / 3. Extending this to the next difference gives 3, and therefore the next term 184, so the solution is consistent.

Why Other Options Are Wrong:
- Option 188 would require a difference of 7 from 181, which does not fit the geometric pattern. - Option 198 would require a difference of 17, again inconsistent with multiplying by -1 / 3. - Option 221 requires a much larger jump and clearly breaks the established structure.

Common Pitfalls:
Many learners only look for additive or subtractive patterns directly on the main series and may not think to inspect the differences themselves. Others may calculate one of the differences incorrectly, making the geometric pattern harder to see. Careful computation and a willingness to examine second level patterns are important.

Final Answer:
The missing term in the series is 184, so the correct option is 184.