A series is given with one number missing. Choose the correct alternative that will complete the decimal number series: 4, 5.2, 6.4, ?, 8.8.

Introduction / Context:
This question involves a number series with decimal values. The aim is to identify the pattern by which each term is obtained from the previous one and then use that rule to find the missing term. Decimal series questions test both comfort with fractions and the ability to notice small, consistent changes between terms.

Given Data / Assumptions:

- The given series is 4, 5.2, 6.4, ?, 8.8.- One term is missing between 6.4 and 8.8.- The same rule is applied throughout the series.

Concept / Approach:
Because the numbers are close together and increase smoothly, the most likely rule is that we add a constant decimal value to each term. Therefore, we should compute the differences between the given adjacent terms. If those differences are equal or follow a simple pattern, we can apply that difference to obtain the missing term.

Step-by-Step Solution:
Step 1: Calculate the difference between the second and first terms: 5.2 - 4 = 1.2.Step 2: Calculate the difference between the third and second terms: 6.4 - 5.2 = 1.2.Step 3: So far, the common difference is 1.2.Step 4: Assume the same difference continues. The missing term after 6.4 should be 6.4 + 1.2 = 7.6.Step 5: Check the last gap using this value: 8.8 - 7.6 = 1.2, which matches the same difference.Step 6: Therefore the missing term that keeps a constant increment of 1.2 is 7.6.

Verification / Alternative check:
The completed series becomes 4, 5.2, 6.4, 7.6, 8.8. Now check each difference: 5.2 - 4 = 1.2, 6.4 - 5.2 = 1.2, 7.6 - 6.4 = 1.2 and 8.8 - 7.6 = 1.2. Since the common difference is uniform throughout, this confirms that our answer is consistent and correct.

Why Other Options Are Wrong:
If we choose 7, the difference from 6.4 is 0.6 and from 7 to 8.8 is 1.8, which does not preserve a constant increase. Option 8 gives differences of 1.6 and 0.8, also inconsistent. Option 8.25 creates uneven jumps as well. Thus, none of these values can form a simple arithmetic progression in decimals, so they must be rejected.

Common Pitfalls:
Some test takers become nervous when they see decimals and try to convert them to fractions or use unnecessary calculations. The key idea is that the method of looking at differences remains the same whether the numbers are integers or decimals. Focus on the pattern, not on the type of numbers used.

Final Answer:
The missing decimal number that completes the series is 7.6.