Find the common ratio for the geometric sequence.
$0.8,0.12,0.018,0.0027,\dots$

• A. $0.68$
• B. $6.67$
• C. $0.15$
• D. $0.0034$

Answer: (C)

Verified step by step guidance

1. Identify the terms of the geometric sequence given: \(0.8, 0.12, 0.018, 0.0027, \dots\)
2. Recall that the common ratio \(r\) in a geometric sequence is found by dividing any term by the previous term, so \(r = \frac{a_{n+1}}{a_n}\).
3. Calculate the ratio using the first two terms: \(r = \frac{0.12}{0.8}\).
4. Simplify the fraction to find the value of \(r\) without performing the final division.
5. Verify the ratio by checking if \(\frac{0.018}{0.12}\) and \(\frac{0.0027}{0.018}\) give the same value of \(r\) to confirm the sequence is geometric.