Understanding the Number Series Pattern

This question asks us to find the next number in a given series: 12.8, 13.5, 14.9, 17, ?. To solve this, we need to identify the pattern or rule that connects the numbers in the sequence.

Let's look at the difference between consecutive terms:

• Difference between the second and first term: $\text{13.5 - 12.8 = 0.7}$
• Difference between the third and second term: $\text{14.9 - 13.5 = 1.4}$
• Difference between the fourth and third term: $\text{17 - 14.9 = 2.1}$

Analyzing the Differences

The differences we calculated are 0.7, 1.4, and 2.1. Let's look at the differences between these differences:

• Difference between 1.4 and 0.7: $\text{1.4 - 0.7 = 0.7}$
• Difference between 2.1 and 1.4: $\text{2.1 - 1.4 = 0.7}$

We can see that the differences between consecutive terms (0.7, 1.4, 2.1) are increasing by a constant value of 0.7 each time. This indicates that the series is following a pattern where the increment added to each term is itself part of an arithmetic progression.

Predicting the Next Term in the Series

Following the pattern of the differences (0.7, 1.4, 2.1), the next difference should be $2.1 + 0.7 = 2.8$.

To find the next number in the original series, we add this next predicted difference (2.8) to the last number in the series (17).

Next term = Last term + Next difference

Next term = $\text{17 + 2.8}$

Next term = $\text{19.8}$

Conclusion

Based on the pattern identified, the number that replaces the question mark (?) is 19.8.

Revision Table: Key Concepts

Additional Information on Number Series Questions

Number series questions are common in logical reasoning and quantitative aptitude tests. They assess your ability to identify patterns quickly. Common patterns include:

• Arithmetic Progression (constant difference).
• Geometric Progression (constant ratio).
• Differences forming an AP or GP (like in this question).
• Squares or cubes of natural numbers.
• Prime numbers.
• Fibonacci series (sum of two preceding terms).
• Alternating patterns.
• Combination of multiple patterns.

Practicing different types of series helps improve pattern recognition skills.