To find the next term in a geometric sequence, you need to know the common ratio, which is the factor by which each term is multiplied to get the next term. You can find this ratio by dividing any term by the previous term.
For example, if you have a geometric sequence like 2, 6, 18, the common ratio can be calculated as follows:
- 6 ÷ 2 = 3
- 18 ÷ 6 = 3
Now that we know the common ratio is 3, we can find the next term by multiplying the last known term (18) by the common ratio:
- Next term = 18 × 3 = 54
So the next term in this geometric sequence is 54.