In the series 111, 107.5, 104, ?, 97, 93.5, which number should replace the question mark to preserve the pattern?

Introduction / Context:
This question features a decreasing number series with fractional values. The pattern is actually very simple: a constant negative difference is applied at each step. The task is to identify this constant difference and then use it to compute the missing value in the middle of the sequence.

Given Data / Assumptions:
- The series is: 111, 107.5, 104, ?, 97, 93.5.- Values are decreasing but by the same amount each time.- The common difference appears to be a decimal number.

Concept / Approach:
We compute the difference between consecutive known terms and check whether it remains constant. If it does, we apply the same difference between 104 and the missing term, and between the missing term and 97, to maintain a perfect arithmetic progression. This straightforward approach handles both integer and decimal progressions effectively.

Step-by-Step Solution:
- Difference from 111 to 107.5: 111 - 107.5 = 3.5.- Difference from 107.5 to 104: 107.5 - 104 = 3.5.- So the common difference is -3.5 at each step.- Apply the same difference to find the missing term after 104.- 104 - 3.5 = 100.5.- Now check from 100.5 to 97: 100.5 - 97 = 3.5, which is consistent.- 97 - 3.5 = 93.5, which matches the last term in the series.

Verification / Alternative check:
- Write the full arithmetic progression: 111, 107.5, 104, 100.5, 97, 93.5.- Confirm that each step decreases by exactly 3.5.- Since the pattern is uniform and consistent, 100.5 must be the missing term.

Why Other Options Are Wrong:
- 100 or 99 would create differences of 4 or 5 with neighbouring terms, breaking the constant -3.5 step.- 99.5 would also produce inconsistent differences between 104 and the missing term, and between the missing term and 97.- Only 100.5 maintains a uniform difference of -3.5 throughout the series.

Common Pitfalls:
Some candidates miscalculate decimal differences or assume that the series must involve more complex operations. Others may attempt to use multiplication even when the changes are small and consistent. For such sequences, always test for a simple arithmetic progression first, even when the numbers are decimals.

Final Answer:
The correct number to fill the blank is 100.5, so the correct option is 100.5.