What is the next term in the geometric series: 3, 6, 12, ...?

In a geometric series, each term is found by multiplying the previous term by a constant ratio. To identify the next term in the series 3, 6, 12, we first need to find that ratio.

Looking at the series, the first term is 3, and the second term is 6. We can calculate the ratio by dividing the second term by the first term:

6 / 3 = 2.

Next, we can check the ratio between the second term and the third term:

12 / 6 = 2.

Since both pairs yield the same ratio of 2, we can conclude that the series has a common ratio of 2.

To determine the next term after 12, we multiply the last known term (12) by this common ratio (2):

12 * 2 = 24.

Thus, the next term in the series is 24.