A series is given with one number missing. Choose the correct alternative from the given ones that will complete the series: -7.25, -5.75, -4.25, -2.75, ?, 0.25.

Introduction / Context:
This is an arithmetic sequence involving negative decimals where each term increases by the same fixed amount. The task is to find the missing term in the middle. Such questions test basic understanding of arithmetic progressions and comfort with decimal addition and subtraction, particularly involving negative values.

Given Data / Assumptions:

• Series: -7.25, -5.75, -4.25, -2.75, ?, 0.25.
• One term is missing between -2.75 and 0.25.
• The numbers appear to increase by a constant decimal step.

Concept / Approach:
In an arithmetic progression, each term differs from the previous one by a constant value known as the common difference. Here, we calculate the difference between any two consecutive known terms to determine that common difference. Once we know the step size, we can move forward or backward to fill in the missing term. Working carefully with decimals is important to avoid small arithmetic mistakes.

Step-by-Step Solution:
Step 1: Compute the difference between the first two terms. -5.75 - (-7.25) = -5.75 + 7.25 = 1.5. Step 2: Compute the next difference to confirm it is constant. -4.25 - (-5.75) = -4.25 + 5.75 = 1.5. Step 3: Check once more. -2.75 - (-4.25) = -2.75 + 4.25 = 1.5. Step 4: Therefore, the common difference of the arithmetic sequence is +1.5. Step 5: To find the missing term after -2.75, add 1.5. -2.75 + 1.5 = -1.25.

Verification / Alternative check:
Now include the missing term and check the entire progression: -7.25, -5.75, -4.25, -2.75, -1.25, 0.25. Compute all differences: each step gives +1.5. That is, -5.75 - (-7.25) = 1.5, -4.25 - (-5.75) = 1.5, -2.75 - (-4.25) = 1.5, -1.25 - (-2.75) = 1.5, and 0.25 - (-1.25) = 1.5. This confirms that the entire series is a regular arithmetic progression with common difference 1.5.

Why Other Options Are Wrong:
Values 1.25 and 1.5 are positive and would place the missing term on the wrong side of zero, breaking the constant step between -2.75 and 0.25. Value -1.5 would create a difference of +1.25 from -2.75 instead of +1.5, again ruining the constant difference property. Only -1.25 preserves the same increment of 1.5 that we observe between all other consecutive terms.

Common Pitfalls:
Some students mishandle the negative signs and decimals, especially when subtracting a negative number. Others may guess based on approximate spacing without actually computing the exact difference. The safest method is always to calculate the difference between terms explicitly, paying attention to signs and decimal places, and then check that the same difference works throughout the series.

Final Answer:
The missing number that completes the arithmetic sequence is -1.25.