In the following number series with negative and positive fractional values, one term is missing. Carefully observe the pattern in -7/4, -1, -0.25, ?, 5/4, 2 and choose the correct alternative that completes the series.

Introduction / Context:
This question presents a number series involving a smooth transition from negative fractions to positive values. The given series is -7/4, -1, -0.25, ?, 5/4, 2. The objective is to understand the pattern that governs these changes and then find the missing term. Such questions test a candidate's comfort with fractions, decimals, and arithmetic progressions, especially when signs change from negative to positive.

Given Data / Assumptions:
Given series: -7/4, -1, -0.25, ?, 5/4, 2.
We can represent the numbers in decimal form for easier comparison.
There should be a single consistent rule applied across the series.
The missing value must fit between -0.25 and 5/4 without breaking the pattern.

Concept / Approach:
First, convert the fractions to decimals: -7/4 = -1.75, -1 remains -1.00, -0.25 is already in decimal form, 5/4 = 1.25, and 2 is 2.00. Now the series becomes -1.75, -1.00, -0.25, ?, 1.25, 2.00. Observing the differences suggests that the sequence might be an arithmetic progression with a constant increment. The difference from -1.75 to -1.00 is +0.75, and from -1.00 to -0.25 is again +0.75. This indicates a common difference of 0.75 throughout the series.

Step-by-Step Solution:
Write the series in decimals: -1.75, -1.00, -0.25, ?, 1.25, 2.00. Difference from -1.75 to -1.00 is +0.75. Difference from -1.00 to -0.25 is +0.75 again. Add 0.75 to -0.25 to obtain the missing term: -0.25 + 0.75 = 0.50. Next, 0.50 + 0.75 = 1.25 and 1.25 + 0.75 = 2.00, which match the given later terms. Thus, the missing term is 0.5.

Verification / Alternative check:
We can verify the pattern by checking each step. The constant increment is 0.75 from the first to the last term. Using this single rule reproduces all given numbers perfectly when we insert 0.5 in the missing slot. If we try any other candidate, the difference sequence will break, proving that 0.5 is the only value that maintains the arithmetic progression.

Why Other Options Are Wrong:
Option B: 0.75 would give a step of 1.00 between -0.25 and 0.75, which is inconsistent with earlier differences.
Option C: 0.25 would create a difference of only 0.50 from -0.25, again breaking the constant increment of 0.75.
Option D: 1.00 jumps too far and does not maintain the regular pattern around 1.25 and 2.00.
Option E: 1.5 leads to an even more irregular jump and cannot form a consistent arithmetic sequence.

Common Pitfalls:
Students sometimes ignore decimal conversions and try to work directly with fractions, which can hide the simple arithmetic progression. Others may be distracted by the change from negative to positive and assume that the rule is complicated. In reality, the entire series follows a uniform step size. Recognising that a series can cross zero while still using a constant difference is important for correctly solving such problems.

Final Answer:
The number that completes the series while maintaining a constant step of 0.75 is 0.5, so the correct option is 0.5.