ANSWER
The common ratio for the geometric sequence is
[tex]r = \frac{2}{3} [/tex]
EXPLANATION
The given geometric sequence is
[tex]54,36,24,16...[/tex]
We can determine the common ratio using any two consecutive terms.
The common ratio is found by expressing the subsequent term over the previous term and simplifying the result.
The common ratio is given by,
[tex]r = \frac{36}{54} = \frac{2}{3} [/tex]
Or
[tex]r = \frac{24}{36} = \frac{2}{3} [/tex]
Or
[tex]r = \frac{16}{24} = \frac{2}{3} [/tex]
