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

• A. $3$
• B. $\frac{1}{3}$
• C. $\frac{1}{5}$
• D. $-\frac{12}{5}$

Answer: (B)

Verified step by step guidance

1. Recall that the common ratio \( r \) in a geometric sequence is found by dividing any term by the previous term. This means \( r = \frac{a_{n+1}}{a_n} \), where \( a_n \) is the \( n^{th} \) term.
2. Identify the first two terms of the sequence: \( a_1 = \frac{18}{5} \) and \( a_2 = \frac{6}{5} \).
3. Calculate the ratio \( r \) by dividing the second term by 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 expression by canceling common factors to find the common ratio \( r \).