A series is given, with one number missing. Choose the correct alternative from the given ones that will complete the series: 99, 90.7, 82.4, ?, 65.8, 57.5.

Introduction / Context:
This is a decimal number series that decreases by the same amount at each step. Your task is to identify the constant decrement and then use it to compute the missing term in the middle. Decimal based arithmetic progressions like this are used to test precision in calculation and familiarity with decimal subtraction.

Given Data / Assumptions:

• Series: 99, 90.7, 82.4, ?, 65.8, 57.5.
• One term is missing between 82.4 and 65.8.
• The series appears to decrease smoothly by a fixed decimal amount.

Concept / Approach:
To solve this, compute the difference between two consecutive known terms and check whether the same difference applies repeatedly. If the common difference is constant, the series is an arithmetic progression. We can then move forward or backward by adding or subtracting this difference to determine any missing term. Careful handling of decimals is required to avoid errors.

Step-by-Step Solution:
Step 1: Compute the difference between the first two terms. 90.7 - 99 = -8.3, so the series decreases by 8.3 from 99 to 90.7. Step 2: Compute the difference between the next two visible terms to confirm the pattern. 82.4 - 90.7 = -8.3. Step 3: We see a constant difference of -8.3 between these consecutive terms. Step 4: To find the term after 82.4, subtract 8.3 again. 82.4 - 8.3 = 74.1. Step 5: Check that this same difference continues to the later terms. 65.8 - 74.1 = -8.3, and 57.5 - 65.8 = -8.3, confirming the consistency.

Verification / Alternative check:
Insert the computed term into the series: 99, 90.7, 82.4, 74.1, 65.8, 57.5. Now verify all differences: 90.7 - 99 = -8.3, 82.4 - 90.7 = -8.3, 74.1 - 82.4 = -8.3, 65.8 - 74.1 = -8.3, and 57.5 - 65.8 = -8.3. Every step uses the same decrement, so the series is a perfect arithmetic progression with common difference -8.3, confirming that 74.1 is the correct missing term.

Why Other Options Are Wrong:
Options 73.3, 74.8, and 75.2 would each produce at least one difference that is not equal to -8.3. For example, if the missing term were 73.3, then 73.3 - 82.4 = -9.1, which does not match the observed pattern. Any deviation from the constant step of -8.3 would break the arithmetic progression, so these values cannot be correct.

Common Pitfalls:
Some learners approximate the decimal differences mentally and may incorrectly assume a slightly different step size, such as -8 or -9. Others may only check differences at the beginning of the series and not confirm them for all later terms. The safest approach is to compute all relevant differences accurately and ensure that the same value appears throughout the sequence.

Final Answer:
The number that correctly completes the decimal series is 74.1.