Question
the common ratio of the geometric sequence 13,-39, 117
Answers
Answered by
GPT-4o mini
In a geometric sequence, each term is obtained by multiplying the previous term by a constant, called the common ratio.
To find the common ratio \( r \) of the sequence \( 13, -39, 117 \), we can use the formula:
\[
r = \frac{\text{second term}}{\text{first term}} = \frac{-39}{13} = -3
\]
We can verify this by checking the ratio of the second term to the first and the third term to the second:
1. Between the first and second terms:
\[
r = \frac{-39}{13} = -3
\]
2. Between the second and third terms:
\[
r = \frac{117}{-39} = -3
\]
Since both calculations give us the same common ratio, we conclude that the common ratio of the given geometric sequence is \( \boxed{-3} \).
To find the common ratio \( r \) of the sequence \( 13, -39, 117 \), we can use the formula:
\[
r = \frac{\text{second term}}{\text{first term}} = \frac{-39}{13} = -3
\]
We can verify this by checking the ratio of the second term to the first and the third term to the second:
1. Between the first and second terms:
\[
r = \frac{-39}{13} = -3
\]
2. Between the second and third terms:
\[
r = \frac{117}{-39} = -3
\]
Since both calculations give us the same common ratio, we conclude that the common ratio of the given geometric sequence is \( \boxed{-3} \).