A number series is given below with one term missing. Choose the correct alternative from the given options that will complete the series. 72, 65.7, ?, 53.1, 46.8

Introduction / Context:
This series question tests the understanding of a simple arithmetic progression with a constant negative difference that involves decimal values. The learner needs to identify how much each term decreases and then apply that decrease to determine the missing term. Such questions improve comfort with decimal subtraction and pattern recognition.

Given Data / Assumptions:
- Given series: 72, 65.7, ?, 53.1, 46.8. - The third term is missing. - The pattern is expected to be a constant step between terms.

Concept / Approach:
In an arithmetic progression, each term is obtained by adding or subtracting a fixed value called the common difference. By using the first and last terms and the number of steps between them, or by computing successive differences between adjacent known terms, this common difference can be discovered. Once the difference is known, every missing term can be filled in.

Step-by-Step Solution:
Step 1: Observe the first and last given terms: 72 and 46.8, with four steps between them. Step 2: Compute the total change: 46.8 - 72 = -25.2. Step 3: Divide this change by four steps to find the common difference: -25.2 / 4 = -6.3. Step 4: Check between the first two terms: 72 - 6.3 = 65.7, which matches the series. Step 5: Apply the same difference from the second term to find the missing value: 65.7 - 6.3 = 59.4. Step 6: Continue to verify: 59.4 - 6.3 = 53.1, and 53.1 - 6.3 = 46.8, which confirms the consistency.

Verification / Alternative check:
An alternative method is to compute the difference directly between known adjacent terms: 65.7 to 53.1 is a change of -12.6 over two steps, so the step per term is -12.6 / 2 = -6.3. The same difference connects 53.1 to 46.8. This again confirms that each step is a reduction of 6.3 and confirms 59.4 as the missing value.

Why Other Options Are Wrong:
- Option 60.4 does not maintain a constant difference of -6.3 and would break the smooth progression. - Option 59.3 introduces a small discrepancy and would not give exact equal steps across the series. - Option 60.3 also fails to match a consistent difference when checked against the neighbouring terms.

Common Pitfalls:
Learners may approximate differences mentally and accept near values instead of exact ones, which leads to minor errors that completely break the arithmetic pattern. It is important to carry out calculations accurately, especially with decimal values, and confirm that the same difference works between every pair of adjacent terms.

Final Answer:
The missing term in the series is 59.4, so the correct option is 59.4.