The common ratio of the geometric sequence 13, 91, 637, 4459.

To find the common ratio of a geometric sequence, we divide any term in the sequence by the previous term. Let's calculate the ratio between consecutive terms of the sequence 13, 91, 637, 4459.

1. First ratio:
\[
r = \frac{91}{13} = 7
\]

2. Second ratio:
\[
r = \frac{637}{91} = 7
\]

3. Third ratio:
\[
r = \frac{4459}{637} = 7
\]

Since the ratio between consecutive terms is consistently \(7\), the common ratio \(r\) is 7.

Would you like more details or have any other questions?

Here are 5 related questions:
1. What is the general term formula for a geometric sequence?
2. How do you find the sum of the first \(n\) terms of a geometric sequence?
3. Can the common ratio of a geometric sequence be negative?
4. What happens when the common ratio of a geometric sequence is between 0 and 1?
5. How can you determine if a sequence is geometric from a set of terms?

**Tip:** In a geometric sequence, multiplying the common ratio by one term gives the next term, which makes it easy to predict future terms.

Discover how to find the common ratio of the geometric sequence 13, 91, 637, 4459. This detailed solution explains key concepts such as geometric sequences and the common ratio formula, suitable for students in Grades 9-11.

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