Final answer:
The series 3, 4, 6, 9, 13 increases by 1, 2, 3, and then 4, respectively. Following this pattern, the next increase is by 5, which makes the next number in the series 18.
Step-by-step explanation:
To determine the next number in the series 3, 4, 6, 9, 13, we need to find the pattern that the numbers are following. As we observe:
- 3 to 4 is an increase of 1,
- 4 to 6 is an increase of 2,
- 6 to 9 is an increase of 3,
- 9 to 13 is an increase of 4.
Following this pattern, the difference between the numbers increases by 1 each time. Thus, the next difference should be an increase of 5. If we add 5 to the last number in the series (13), we get 18.
Therefore, the next number in the series is 18.