Select the number from among the given options that can replace the question mark(?) in the following series. 2, 4, 7, 11, 16, 22, ?
29
Solving the Number Series Problem
The question asks us to find the next number in the given series: 2, 4, 7, 11, 16, 22, ?
To solve this, we need to identify the pattern governing the sequence of numbers. Let's look at the differences between consecutive terms in the number series.
Analyzing the Differences in the Number Series
We calculate the difference between each term and the term preceding it:
- Difference between 4 and 2: \(4 - 2 = 2\)
- Difference between 7 and 4: \(7 - 4 = 3\)
- Difference between 11 and 7: \(11 - 7 = 4\)
- Difference between 16 and 11: \(16 - 11 = 5\)
- Difference between 22 and 16: \(22 - 16 = 6\)
Identifying the Pattern
The differences we found are 2, 3, 4, 5, 6. We can observe a clear pattern in these differences: they are consecutive integers starting from 2 and increasing by 1 each time.
Following this pattern, the next difference in the series should be the next integer after 6, which is 7.
Calculating the Next Term in the Series
To find the next number in the original series, we add the next expected difference (7) to the last term in the series (22).
Next term = Last term + Next difference
Next term = $$22 + 7$$
Next term = $$29$$
Therefore, the number that replaces the question mark in the series is 29.
Final Answer
The next number in the series 2, 4, 7, 11, 16, 22, ? is 29.
Revision Table: Number Series Pattern
| Term Number | Term Value | Difference from Previous Term |
|---|---|---|
| 1st | 2 | - |
| 2nd | 4 | \(4 - 2 = 2\) |
| 3rd | 7 | \(7 - 4 = 3\) |
| 4th | 11 | \(11 - 7 = 4\) |
| 5th | 16 | \(16 - 11 = 5\) |
| 6th | 22 | \(22 - 16 = 6\) |
| 7th | ? | Next difference should be 7 |
Additional Information on Number Series
Number series questions are common in aptitude and reasoning tests. They require identifying a specific pattern that relates the terms in the sequence. Common patterns include:
- Arithmetic Progression: A constant difference between consecutive terms.
- Geometric Progression: A constant ratio between consecutive terms.
- Difference Series: The differences between consecutive terms form their own recognizable pattern (as seen in this question).
- Double Difference Series: The differences of the differences form a pattern.
- Squares or Cubes: Terms related to squares or cubes of numbers.
- Fibonacci Series: Each term is the sum of the two preceding ones (e.g., 1, 1, 2, 3, 5, 8...).
- Mixed Series: Combinations of different patterns.
Practicing different types of series helps in quickly recognizing the underlying logic during exams.
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