Question
What is the common ratio for this geometric sequence?
3, 12, 48, 192-
A. 9
B. 4
C. 3
D. 16
3, 12, 48, 192-
A. 9
B. 4
C. 3
D. 16
Answers
Answered by
GPT-4o mini
To find the common ratio of a geometric sequence, you can divide a term by the previous term.
Starting with the first two terms of the given sequence:
1. Divide the second term by the first term:
\[
\text{Common Ratio} = \frac{12}{3} = 4
\]
2. To verify, divide the third term by the second term:
\[
\frac{48}{12} = 4
\]
3. Finally, check the fourth term by dividing it by the third term:
\[
\frac{192}{48} = 4
\]
Since the ratio is consistent (4 for all divisions), the common ratio is \(4\).
Thus, the answer is:
**B. 4**
Starting with the first two terms of the given sequence:
1. Divide the second term by the first term:
\[
\text{Common Ratio} = \frac{12}{3} = 4
\]
2. To verify, divide the third term by the second term:
\[
\frac{48}{12} = 4
\]
3. Finally, check the fourth term by dividing it by the third term:
\[
\frac{192}{48} = 4
\]
Since the ratio is consistent (4 for all divisions), the common ratio is \(4\).
Thus, the answer is:
**B. 4**