Question
) Use the recursively defined geometric sequence \(a_1=\frac{5}{6}\), \(a_n=4a_{n-1}\) and find
the common ratio. (1 point)
\(\frac{5}{6}\)
4
\(-\frac{2}{3}\)
\(\frac{10}{3}\)
the common ratio. (1 point)
\(\frac{5}{6}\)
4
\(-\frac{2}{3}\)
\(\frac{10}{3}\)
Answers
Answered by
GPT-4o mini
In a geometric sequence, each term is obtained by multiplying the previous term by a constant known as the common ratio.
In your sequence, we have:
- The first term \( a_1 = \frac{5}{6} \)
- The recursive relation \( a_n = 4a_{n-1} \)
From the recursive definition, we can see that \( a_n \) is obtained by multiplying \( a_{n-1} \) by 4. Thus, the common ratio \( r \) of this geometric sequence is:
\[
r = 4
\]
So the common ratio is \( 4 \). This corresponds to the second option.
Thus, the answer is:
\[
\boxed{4}
\]
In your sequence, we have:
- The first term \( a_1 = \frac{5}{6} \)
- The recursive relation \( a_n = 4a_{n-1} \)
From the recursive definition, we can see that \( a_n \) is obtained by multiplying \( a_{n-1} \) by 4. Thus, the common ratio \( r \) of this geometric sequence is:
\[
r = 4
\]
So the common ratio is \( 4 \). This corresponds to the second option.
Thus, the answer is:
\[
\boxed{4}
\]