The next number in the series 5, 11, 19 is 29.
Here's how we arrive at that answer:
Analyzing the Differences
First, we analyze the differences between consecutive numbers in the series.
- 11 - 5 = 6
- 19 - 11 = 8
We can observe a pattern in the differences: 6 and 8.
Identifying the Pattern
The differences between the numbers (6 and 8) form an arithmetic sequence where each subsequent term is increased by two:
- The difference between 11 and 5 is 6.
- The difference between 19 and 11 is 8.
- The difference between 8 and 6 is 2. This is where we identify the pattern of even numbers.
Calculating the Next Difference
Following the pattern of even numbers, the next difference would be 8 + 2 = 10
Calculating the Next Number
To get the next number in the series we add 10 to the last number in the series which is 19. 19 + 10 = 29.
Therefore, the next number in the series is 29.
| Position | Number | Difference | Difference of Difference |
|---|---|---|---|
| 1 | 5 | ||
| 2 | 11 | 6 | |
| 3 | 19 | 8 | 2 |
| 4 | 29 | 10 | 2 |
Summary
- The original series is: 5, 11, 19...
- The differences between consecutive numbers are: 6, 8...
- The differences form an arithmetic series where the common difference is 2, meaning that the next difference is 10.
- Adding the next difference to the last term gives the following number in the series, 19 + 10 = 29.
