Find the common ratio for the geometric sequence.
$3,12,48,192,\dots$

• A. $3$
• B. $4$
• C. $6$
• D. $9$

Answer: (B)

Verified step by step guidance

1. Identify the terms of the geometric sequence given: 3, 12, 48, 192, ...
2. Recall that the common ratio \( r \) in a geometric sequence is found by dividing any term by the previous term.
3. Calculate the ratio between the second term and the first term using the formula: \( r = \frac{a_2}{a_1} \), where \( a_2 = 12 \) and \( a_1 = 3 \).
4. Verify the common ratio by checking the ratio between the third term and the second term: \( r = \frac{a_3}{a_2} \), where \( a_3 = 48 \) and \( a_2 = 12 \).
5. Confirm that the ratio is consistent for the next terms to ensure it is the common ratio of the sequence.