To find the next two terms of the geometric sequence given (3, 6, 12), we need to determine the common ratio (r) first. In a geometric sequence, each term is found by multiplying the previous term by the common ratio.
1. Calculate the common ratio (r):
- Divide the second term by the first term: 6 ÷ 3 = 2
- Divide the third term by the second term: 12 ÷ 6 = 2
- Since both results are equal to 2, the common ratio (r) is 2.
2. Find the fourth term:
- Multiply the third term by the common ratio: 12 * 2 = 24
- Therefore, the fourth term of the sequence is 24.
3. Find the fifth term:
- To find the fifth term, multiply the fourth term by the common ratio: 24 * 2 = 48
- Hence, the fifth term of the sequence is 48.
Therefore, the next two terms of the given geometric sequence (3, 6, 12) are 24 and 48.
