Find the missing number in the given series.
0.2
Finding the Missing Number in a Series
The question asks us to identify the missing term in the given number series:
-1.3, -0.8, -0.3, ?, 0.7, 1.2
Analyzing the Number Series Pattern
Let's examine the relationship between consecutive terms in the series. We can calculate the difference between each term and the one preceding it.
- Difference between the second and first term: \[-0.8 - (-1.3) = -0.8 + 1.3 = 0.5\]
- Difference between the third and second term: \[-0.3 - (-0.8) = -0.3 + 0.8 = 0.5\]
We observe a consistent difference of 0.5 between the terms we have checked so far. This suggests that the series is an arithmetic progression with a common difference of 0.5.
Calculating the Missing Term
Assuming the pattern of adding 0.5 continues, the missing term should be obtained by adding 0.5 to the third term (-0.3).
Missing term = Third term + Common difference
Missing term = \[-0.3 + 0.5 = 0.2\]
Verifying the Pattern
Let's check if adding the common difference (0.5) to our calculated missing term (0.2) gives the next term in the series (0.7).
Calculated missing term + Common difference = \[0.2 + 0.5 = 0.7\]
This matches the fifth term in the given series (0.7), confirming our calculated missing number and the pattern.
Conclusion on the Missing Number
Based on the analysis, the missing number in the series -1.3, -0.8, -0.3, ?, 0.7, 1.2 is 0.2.
| Term Position | Term Value | Difference from Previous Term |
|---|---|---|
| 1st | -1.3 | - |
| 2nd | -0.8 | -0.8 - (-1.3) = 0.5 |
| 3rd | -0.3 | -0.3 - (-0.8) = 0.5 |
| 4th (Missing) | 0.2 | 0.2 - (-0.3) = 0.5 |
| 5th | 0.7 | 0.7 - 0.2 = 0.5 |
| 6th | 1.2 | 1.2 - 0.7 = 0.5 |
Revision Table: Number Series Concepts
| Concept | Description |
|---|---|
| Number Series | A sequence of numbers that follow a specific pattern or rule. |
| Arithmetic Progression (AP) | A sequence where the difference between consecutive terms is constant (called the common difference). |
| Common Difference | The constant value added to each term to get the next term in an arithmetic progression. |
Additional Information: Solving Number Series Questions
Solving number series questions often involves identifying the underlying pattern. Common patterns include:
- Arithmetic progressions (constant difference).
- Geometric progressions (constant ratio).
- Differences between terms forming another pattern (e.g., squares, cubes, prime numbers).
- Alternating patterns.
- Patterns involving multiplication, division, squares, cubes, etc.
To solve these questions, start by finding the differences or ratios between consecutive terms. If a simple pattern isn't obvious, look at the differences of the differences, or consider other operations like multiplication, division, or sequences of squares/cubes.
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