To find the next three terms in the sequence 8, 24, 72, 216, we first need to examine how the terms are related to each other.
We can look at the ratios between consecutive terms:
- 24 / 8 = 3
- 72 / 24 = 3
- 216 / 72 = 3
From this observation, we can see that each term can be obtained by multiplying the previous term by 3. To confirm, we can express the sequence as follows:
- 1st term: 8
- 2nd term: 8 × 3 = 24
- 3rd term: 24 × 3 = 72
- 4th term: 72 × 3 = 216
Now, let’s find the next three terms:
- 5th term: 216 × 3 = 648
- 6th term: 648 × 3 = 1944
- 7th term: 1944 × 3 = 5832
Thus, the next three terms in the sequence are 648, 1944, and 5832.