In the following question, select the missing number from the given series. 69, 70, 73, 78, 85, ?
94
Solving the Number Series Question
The question asks us to find the missing number in the given series: 69, 70, 73, 78, 85, ?
To solve a number series problem, we need to identify the pattern or rule that governs the sequence of numbers. Let's look at the difference between consecutive terms in the series.
- Difference between the 2nd and 1st term: $70 - 69 = 1$
- Difference between the 3rd and 2nd term: $73 - 70 = 3$
- Difference between the 4th and 3rd term: $78 - 73 = 5$
- Difference between the 5th and 4th term: $85 - 78 = 7$
Let's list the differences we found:
| Terms | Difference |
|---|---|
| 70 - 69 | 1 |
| 73 - 70 | 3 |
| 78 - 73 | 5 |
| 85 - 78 | 7 |
Observing the differences (1, 3, 5, 7), we can see a clear pattern. These are consecutive odd numbers starting from 1. The next difference in this sequence of odd numbers should be the next odd number after 7, which is 9.
To find the missing number in the series, we add this next difference (9) to the last term of the given series (85).
Missing number = Last term + Next difference
Missing number = $85 + 9$
Missing number = $94$
So, the missing number in the series is 94.
Let's check the given options:
- 94
- 90
- 85
- 76
The calculated missing number, 94, matches Option 1.
Therefore, the complete series is 69, 70, 73, 78, 85, 94.
Revision Table: Understanding Number Series
| Concept | Description |
|---|---|
| Number Series | A sequence of numbers that follow a specific pattern or rule. |
| Pattern Recognition | The key skill needed to solve number series problems, often involving differences, ratios, squares, cubes, or other mathematical operations between terms. |
| Difference Method | Calculating the difference between consecutive terms to find a pattern in the differences themselves. |
| Identifying the Rule | Once differences or ratios are found, look for sequences like arithmetic progression, geometric progression, squares, cubes, prime numbers, odd/even numbers, etc. |
Additional Information on Number Series Questions
Number series questions are common in various competitive exams and aptitude tests. They assess your logical reasoning and mathematical skills. Here are some common types of patterns found in number series:
- Arithmetic Progression: The difference between consecutive terms is constant. Example: 2, 5, 8, 11, ... (difference is 3)
- Geometric Progression: The ratio between consecutive terms is constant. Example: 3, 6, 12, 24, ... (ratio is 2)
- Difference Series: The differences between consecutive terms form a pattern (like the odd number series in our problem).
- Square or Cube Series: Terms are squares or cubes of natural numbers, or related to them. Example: 1, 4, 9, 16, ... (squares of 1, 2, 3, 4)
- Mixed Series: A combination of two or more patterns, or alternating patterns. Example: 1, 5, 2, 6, 3, 7, ... (alternating +4, -3)
- Fibonacci Series: Each term is the sum of the two preceding terms. Example: 1, 1, 2, 3, 5, 8, ...
When solving a number series, always start by calculating differences. If differences don't show a simple pattern, try ratios or other relationships between terms.
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