To determine the pattern in the given series, let's examine the differences between consecutive terms:
3, 9, 6, 12, 9, 15, 12, 18
The differences between consecutive terms are:
6 - 3 = 3
12 - 6 = 6
9 - 12 = -3
15 - 9 = 6
12 - 15 = -3
18 - 12 = 6
Looking at the differences, we observe that they alternate between 3 and 6.
Now, let's look at the given options:
A. 17
B. 15
C. 14
D. 18
Based on the pattern we observed, the next difference should be 3. Therefore, the next number in the series should be the previous term (18) plus the next difference (3), which gives us 21. However, 21 is not one of the available options.
Since 21 is not available, we need to consider the second possibility, which is that the series alternates between 3 and 6. In this case, the next number in the series should be 18 + 3 = 21. Again, 21 is not one of the available options.
Therefore, neither of the patterns we observed in the differences seem to continue in the series. This suggests that the series may not follow a simple mathematical pattern and may instead be a pattern based on a different rule or logic.
As a result, we cannot determine the next number in the series with certainty. However, based on the given options, the closest option to the potential pattern is B. 15.