Question

the ratio of the sequence 27, 9, 3, 1,...

Explanation:

Step1: Define geometric sequence ratio

The ratio $r$ of a geometric sequence is found by dividing any term by the previous term.

Step2: Calculate ratio with first two terms

Take the second term divided by the first term:
$r = \frac{9}{27}$

Step3: Simplify the fraction

Reduce the fraction to lowest terms:
$r = \frac{1}{3}$
(Verify with other consecutive terms: $\frac{3}{9} = \frac{1}{3}$, $\frac{1}{3} = \frac{1}{3}$, confirming consistency)

Answer:

$\frac{1}{3}$