In the following question, select the missing number from the given series. 32, 35, 39, 42, 46, 49, ?
53
Finding the Missing Number in a Series
This question asks us to identify the missing number in a given series: 32, 35, 39, 42, 46, 49, ? To solve this, we need to find the pattern or rule that governs the sequence of numbers.
Analyzing the Number Series Pattern
Let's look at the difference between consecutive terms in the series:
- Difference between the 2nd and 1st term: \(35 - 32 = 3\)
- Difference between the 3rd and 2nd term: \(39 - 35 = 4\)
- Difference between the 4th and 3rd term: \(42 - 39 = 3\)
- Difference between the 5th and 4th term: \(46 - 42 = 4\)
- Difference between the 6th and 5th term: \(49 - 46 = 3\)
From these calculations, we can see a clear pattern in the differences between consecutive terms. The pattern of differences alternates between adding 3 and adding 4.
Applying the Pattern to Find the Missing Number
The differences observed are +3, +4, +3, +4, +3. Following this alternating pattern, the next difference should be +4.
The last known term in the series is 49. To find the missing number, we add the next difference (+4) to the last term:
\(49 + 4 = 53\)
Therefore, the missing number in the series is 53.
Verification of the Series Pattern
Let's write out the series with the pattern applied:
- Start with 32
- \(32 + 3 = 35\)
- \(35 + 4 = 39\)
- \(39 + 3 = 42\)
- \(42 + 4 = 46\)
- \(46 + 3 = 49\)
- \(49 + 4 = 53\)
The series is 32, 35, 39, 42, 46, 49, 53, which matches the given terms and successfully predicts the next term based on the identified +3, +4 alternating addition pattern.
| Term | Value | Difference from Previous Term |
|---|---|---|
| 1st | 32 | - |
| 2nd | 35 | +3 (\(35-32\)) |
| 3rd | 39 | +4 (\(39-35\)) |
| 4th | 42 | +3 (\(42-39\)) |
| 5th | 46 | +4 (\(46-42\)) |
| 6th | 49 | +3 (\(49-46\)) |
| 7th (Missing) | 53 | +4 (\(53-49\)) |
The missing number is indeed 53.
Revision Table: Number Series Analysis
| Concept | Description |
|---|---|
| Pattern Identification | Finding the underlying rule (addition, subtraction, multiplication, division, squares, cubes, etc.) that connects the terms in a series. |
| Difference Series | Examining the differences between consecutive terms to find a pattern. This is useful for arithmetic and some non-arithmetic series. |
| Alternating Patterns | Patterns where the operation or value changes in a repeating sequence (e.g., +3, +4, +3, +4...). |
Additional Information: Types of Number Series
Number series questions are common in aptitude tests. Understanding different types of patterns can help in solving them.
- Arithmetic Series: Each term is obtained by adding a constant value (common difference) to the previous term. Example: 2, 4, 6, 8... (common difference is 2).
- Geometric Series: Each term is obtained by multiplying the previous term by a constant value (common ratio). Example: 3, 9, 27, 81... (common ratio is 3).
- Difference Series: The differences between consecutive terms follow a pattern (like in this question).
- Mixed Series: Series that involve more than one pattern or operation.
- Fibonacci Series: Each term is the sum of the two preceding terms (starting usually with 0, 1 or 1, 1). Example: 0, 1, 1, 2, 3, 5, 8...
- Square/Cube Series: Terms are squares or cubes of numbers, or related to them. Example: 1, 4, 9, 16... (squares of 1, 2, 3, 4...).
Solving number series problems requires careful observation and systematic analysis of the relationship between terms.
Important Questions from Number Series
Select the number from among the given options that can replace the question mark (?) in the following series.
37, 52, 74, 104, 143, ?
Select the number that can replace the question mark (?) in the following series.
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10, 14, 31, 35, 73, 77, ?
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215, 231, 256, 292, ?
Select the number from among the given options that can replace the question mark (?) in the following series.
6, 6, 8, 24, 28, 140, ?
