In the following question, select the missing number from the given series.
40
Finding the Missing Number in a Number Series
Let's analyze the given number series to find the missing term: 43, 45, 42, 46, 41, 47, ?
To solve a number series problem, we need to identify the pattern or rule that connects the terms in the sequence.
Let's look at the differences or relationships between consecutive numbers:
- From 43 to 45: $45 - 43 = +2$
- From 45 to 42: $42 - 45 = -3$
- From 42 to 46: $46 - 42 = +4$
- From 46 to 41: $41 - 46 = -5$
- From 41 to 47: $47 - 41 = +6$
Observing the pattern of the differences, we see a sequence of operations: $+2, -3, +4, -5, +6$.
The pattern involves alternating between addition and subtraction. The number being added or subtracted increases by 1 at each step (2, 3, 4, 5, 6...).
Following this pattern, the next operation after $+6$ should be subtraction, and the number should be 7. So, the next operation is $-7$.
To find the missing number, we apply the next operation $(-7)$ to the last number in the series, which is 47.
Calculation:
$\text{Missing Number} = 47 - 7$
$\text{Missing Number} = 40$
Therefore, the missing number in the series is 40.
| Step | Numbers | Operation | Difference |
|---|---|---|---|
| 1 | 43, 45 | $45 - 43$ | +2 |
| 2 | 45, 42 | $42 - 45$ | -3 |
| 3 | 42, 46 | $46 - 42$ | +4 |
| 4 | 46, 41 | $41 - 46$ | -5 |
| 5 | 41, 47 | $47 - 41$ | +6 |
| 6 | 47, ? | Next operation: -7 | $47 - 7 = 40$ |
The complete series is 43, 45, 42, 46, 41, 47, 40.
Number Series Revision Table
| Concept | Description | Example Pattern |
|---|---|---|
| Arithmetic Series | Constant difference between consecutive terms. | 5, 10, 15, 20... (+5) |
| Geometric Series | Constant ratio between consecutive terms. | 2, 4, 8, 16... (x2) |
| Difference Series | The differences between terms form a pattern (like this question). | 1, 3, 6, 10... (Differences: +2, +3, +4...) |
| Alternating Series | Operations or patterns alternate between two types. | The series 43, 45, 42, 46, 41, 47, 40 alternates between addition and subtraction with increasing values. |
| Fibonacci Series | Each term is the sum of the two preceding ones. | 0, 1, 1, 2, 3, 5, 8... |
Additional Information on Number Series
Number series questions are common in reasoning and aptitude tests. They require you to observe the sequence of numbers and deduce the underlying rule or pattern that governs their arrangement. Once the pattern is identified, you can use it to predict the next number or find a missing term.
Common types of patterns include:
- Addition or subtraction of a constant value.
- Multiplication or division by a constant value.
- Addition or subtraction of values that follow a pattern (e.g., increasing by 1, doubling, squaring).
- Alternating patterns involving different operations or values.
- Patterns based on squares, cubes, prime numbers, etc.
- Combination of multiple patterns.
Solving number series problems improves logical thinking and pattern recognition skills. It's helpful to practice different types of series to become familiar with common patterns.
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.
17, 19, 22, 27, 34, 45, 58,?Select the number from among the given options that can replace the question mark (?) in the following series.
10, 14, 31, 35, 73, 77, ?
Select the number from among the given options that can replace the question mark (?) in the following series.
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, ?
