Select the number from among the given options that can replace the question mark (?) in the following series 803, 844, 885, 926, ?
967
Understanding Number Series Questions
Number series questions test your ability to identify the pattern or rule governing a sequence of numbers. To solve these, you typically look for differences, ratios, squares, cubes, or a combination of operations between consecutive terms.
Analyzing the Given Number Series
The given number series is: 803, 844, 885, 926, ?
We need to find the number that replaces the question mark by identifying the pattern in this specific series.
Finding the Pattern in the Series
Let's examine the difference between consecutive terms in the series:
- Difference between the second and first term: $844 - 803$
- Difference between the third and second term: $885 - 844$
- Difference between the fourth and third term: $926 - 885$
| Consecutive Terms | Difference |
|---|---|
| $844 - 803$ | $41$ |
| $885 - 844$ | $41$ |
| $926 - 885$ | $41$ |
The difference between each consecutive term is constant and is $41$. This indicates an arithmetic progression where each term is obtained by adding $41$ to the previous term.
The pattern is: Term$_n$ = Term$_{n-1}$ + $41$
Calculating the Missing Term
To find the next term in the series (replacing the question mark), we apply the identified pattern to the last known term, which is $926$.
Missing Term = Last Term + $41$
Missing Term = $926 + 41$
Missing Term = $967$
Verifying the Result with Options
The calculated missing term is $967$. Let's check the given options:
- Option 1: 967
- Option 2: 977
- Option 3: 969
- Option 4: 957
Our calculated value, $967$, matches Option 1.
Conclusion
Based on the constant difference of $41$ between consecutive terms, the next number in the series 803, 844, 885, 926, ? is $967$.
Revision Table: Number Series Analysis
| Term Number | Term Value | Pattern Applied |
|---|---|---|
| 1 | 803 | Starting term |
| 2 | 844 | $803 + 41$ |
| 3 | 885 | $844 + 41$ |
| 4 | 926 | $885 + 41$ |
| 5 | ? | $926 + 41 = 967$ |
Additional Information: Types of Number Series
Number series problems can involve various patterns. Some common types include:
- Arithmetic Series: A constant difference between terms (like in this question).
- Geometric Series: A constant ratio between terms (each term is multiplied by a fixed number).
- Difference Series: The difference between consecutive terms itself follows a pattern (e.g., increasing difference, prime numbers as differences).
- Mixed Series: Involving a combination of operations (e.g., alternating addition and subtraction, multiplication and addition).
- Fibonacci Series: Each term is the sum of the two preceding terms.
- Square/Cube Series: Terms are squares or cubes of numbers, or related to them.
Identifying the pattern is key to solving any number series problem effectively.
Important Questions from Number 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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