Final answer:
The common ratio of the geometric sequence 4, 6, 9, is 1.5, confirmed by dividing any term by the preceding term.
Step-by-step explanation:
The question asks for the common ratio of a geometric sequence. The given sequence is 4, 6, 9, and the common ratio can be determined by dividing any term in the sequence by the previous term. Dividing 6 by 4 gives us 1.5, and to confirm that this is indeed the common ratio, divide 9 by 6, which also gives 1.5. Therefore, the common ratio for the sequence is 1.5.
To express the common ratio in its simplest form, it remains as 1.5 because it is a decimal number that cannot be simplified further. When working with geometric sequences, identifying the common ratio is crucial for understanding the pattern of the sequence and for making predictions about further terms.