Find the common ratio for the geometric sequence.
$\frac{18}{5},\frac{6}{5},\frac{2}{5},\frac{2}{15},\dots$

• A. $3$
• B. $\(\frac\)13$
• C. $\(\frac\)15$
• D. $-\(\frac{12}{5}\)$

Answer: (B)

Verified step by step guidance

1. Identify the terms of the geometric sequence given: \(\frac{18}{5}, \frac{6}{5}, \frac{2}{5}, \frac{2}{15}, \ldots\)
2. Recall that the common ratio \(r\) in a geometric sequence is found by dividing any term by the previous term, i.e., \(r = \frac{a_{n+1}}{a_n}\).
3. Calculate the ratio between the second term and the first term: \(r = \frac{\frac{6}{5}}{\frac{18}{5}}\).
4. Simplify the division of fractions by multiplying the numerator by the reciprocal of the denominator: \(r = \frac{6}{5} \times \frac{5}{18}\).
5. Simplify the resulting expression by canceling common factors to find the common ratio \(r\).