To determine the next three terms in the sequence 8, 24, 72, 216, we need to first identify the pattern or rule governing the sequence.
Let’s analyze the existing terms:
- The first term is 8.
- The second term is 24.
- The third term is 72.
- The fourth term is 216.
We can look at the ratios between the consecutive terms:
- 24 ÷ 8 = 3
- 72 ÷ 24 = 3
- 216 ÷ 72 = 3
It appears that each term is being multiplied by 3 to get the next term. To find the next terms after 216, we will continue applying this multiplication by 3:
- Next term: 216 × 3 = 648
- Next term: 648 × 3 = 1944
- Next term: 1944 × 3 = 5832
Therefore, the next three terms in the sequence are:
- 648
- 1944
- 5832
In summary, the sequence continues as follows: 8, 24, 72, 216, 648, 1944, 5832.