In the following question, select the missing number from the given series. 99986, 99996, 100096, 101096, ?
111096
Analyzing the Number Series Pattern
The question asks us to find the missing number in the given series: 99986, 99996, 100096, 101096, ?.
To find the missing number, we need to identify the pattern or the rule that governs the sequence of numbers in the series.
Step-by-Step Solution to Find the Missing Number
Let's look at the differences between consecutive terms in the series:
- Difference between the second and first term: $99996 - 99986$
- Difference between the third and second term: $100096 - 99996$
- Difference between the fourth and third term: $101096 - 100096$
| Terms | Difference |
|---|---|
| $99996 - 99986$ | $10$ |
| $100096 - 99996$ | $100$ |
| $101096 - 100096$ | $1000$ |
Observing the differences (10, 100, 1000), we can see a clear pattern: each difference is 10 times the previous difference. This suggests the next difference in the series should be $1000 \times 10 = 10000$.
To find the missing number, we add this next difference to the last known term in the series:
Missing Number = Last Term + Next Difference
Missing Number = $101096 + 10000$
Missing Number = $111096$
Therefore, the missing number in the series is 111096.
Verifying the Number Series Pattern
The series follows the pattern where the difference between consecutive terms is a power of 10, increasing by a factor of 10 each time:
- $99986 + 10 = 99996$
- $99996 + 100 = 100096$
- $100096 + 1000 = 101096$
- $101096 + 10000 = 111096$ (The missing term)
The completed series is 99986, 99996, 100096, 101096, 111096.
The missing number is 111096.
| Term | Value | Difference from Previous Term |
|---|---|---|
| 1st | $99986$ | - |
| 2nd | $99996$ | $10$ |
| 3rd | $100096$ | $100$ |
| 4th | $101096$ | $1000$ |
| 5th (Missing) | $111096$ | $10000$ |
Revision Table: Number Series Concepts
| Concept | Description |
|---|---|
| Arithmetic Progression | A series where the difference between consecutive terms is constant. |
| Geometric Progression | A series where the ratio of consecutive terms is constant. |
| Difference Series | A method to find the pattern by looking at the differences between consecutive terms. If the differences form a recognizable series (like AP, GP, or another pattern), it helps predict the next term. |
| Mixed Series | A series that might combine arithmetic, geometric, or other patterns, often in the differences or ratios. |
Additional Information: Solving Number Series Questions
Solving number series questions often involves looking for various types of patterns. These can include:
- Constant difference (Arithmetic Progression).
- Constant ratio (Geometric Progression).
- Increasing or decreasing differences/ratios (as seen in this problem).
- Squares, cubes, square roots, or cube roots of numbers.
- Prime numbers or composite numbers.
- Alternating patterns.
- Combinations of arithmetic and geometric operations.
- Patterns based on digits within the numbers.
A good strategy is to first calculate the differences between consecutive terms. If that doesn't reveal a simple pattern, look at the ratios or calculate the differences of the differences (second-order differences).
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