Select the number from among the given options that can replace the question mark (?) in the following series 803, 844, 885, 926, ?
967
Understanding the Number Series Question
The question asks us to find the next number in the given series: 803, 844, 885, 926, ?. To solve this number series problem, we need to identify the underlying pattern or rule that connects consecutive terms.
Analyzing the Number Series Pattern
Let's examine the difference between consecutive terms in the series.
The difference between the second term (844) and the first term (803) is:
\(844 - 803 = 41\)
The difference between the third term (885) and the second term (844) is:
\(885 - 844 = 41\)
The difference between the fourth term (926) and the third term (885) is:
\(926 - 885 = 41\)
We can observe that the difference between successive terms is constant, which is 41. This indicates that the given series is an arithmetic progression with a common difference of 41.
Calculating the Next Term in the Series
Since the pattern is to add 41 to the previous term to get the next term, we can find the missing number by adding 41 to the last given term (926).
The next term will be:
\(926 + 41 = 967\)
Therefore, the number that replaces the question mark (?) in the series is 967.
Step-by-Step Solution Summary
- Identify the given number series: 803, 844, 885, 926, ?.
- Calculate the difference between consecutive terms to find the pattern.
- Difference between 844 and 803 is 41.
- Difference between 885 and 844 is 41.
- Difference between 926 and 885 is 41.
- The pattern is a constant addition of 41.
- Add 41 to the last term (926) to find the missing number.
- \(926 + 41 = 967\).
- The missing number is 967.
Revision Table: Number Series Concepts
| Series Type | Description | Example Pattern |
|---|---|---|
| Arithmetic Series | Each term is obtained by adding a constant value (common difference) to the previous term. | Adding a constant number (e.g., +5, +10, +41). |
| Geometric Series | Each term is obtained by multiplying the previous term by a constant value (common ratio). | Multiplying by a constant number (e.g., ×2, ×3, ×0.5). |
| Difference Series | The difference between consecutive terms follows a pattern (e.g., arithmetic, increasing differences). | Differences are 2, 4, 6, 8... or 5, 10, 15, 20... |
| Mixed Series | Combines two or more patterns, or uses different operations. | Alternating addition/subtraction, or arithmetic/geometric steps. |
Additional Information on Number Series Patterns
Number series questions often appear in reasoning and quantitative aptitude tests. Identifying the pattern is key to solving them. Common patterns include:
- Constant difference (Arithmetic series).
- Constant ratio (Geometric series).
- Increasing or decreasing differences/ratios.
- Alternating patterns (e.g., add, then subtract; add a constant, then add an increasing number).
- Patterns based on squares or cubes of numbers.
- Fibonacci-like sequences where a term is the sum of the previous two terms.
- Combinations of multiple simple patterns.
Practicing with different types of series helps in quickly recognizing the pattern during exams.
Important Questions from Number Series
Select the number from among the given options that can replace the question mark (?) in the following series.
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Select the number from among the given options that can replace the question mark (?) in the following series.
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