Final answer:
The next term of the geometric sequence 27/6, -9/4, 3, 16/27 is -64/81.
Step-by-step explanation:
The given sequence is 27/6, -9/4, 3, 16/27. To find the next term of the sequence, we need to determine the common ratio. The common ratio can be found by dividing any term by the previous term. For example, the common ratio between -9/4 and 3 is 3 / (-9/4) = -4/3.
To find the next term, multiply the last term (16/27) by the common ratio (-4/3). This gives us (16/27) * (-4/3) = -64/81. Therefore, the next term of the sequence is -64/81.