Answer:
121.5, 364.5, 1093.5
Explanation:
In this problem, we are asked to find the next three terms of the given geometric sequence.
To solve this simply, we can first identify the change, or difference, between the sequence's terms.
1.5, 4.5, 13.5, 40.5, ...
From 1.5 to 4.5, the difference is 3.
From 4.5 to 13.5, the difference is 9.
From 13.5 to 40.5, the difference is 27.
We can see that the difference between each term is one more power of three each time. So, we can continue the pattern.
For the next three terms, the difference from the previous term will be be 3 times the previous difference.
So, the differences will be: 81, 243, and 729.
We can add these numbers in a recursive sequence to get the next three terms of the sequence:
40.5 + 81 = 121.5
121.5 + 243 = 364.5
364.5 + 729 = 1093.5