https://file.aiquickdraw.com/mathbot/file/17264384247208hhy4pkd.jpg

The sequence shown in the image is:

\[
1, 5, 25, 125, 625
\]

This is a geometric sequence where each term after the first is obtained by multiplying the previous term by 5. Here's how it works:

\[
1 \times 5 = 5
\]
\[
5 \times 5 = 25
\]
\[
25 \times 5 = 125
\]
\[
125 \times 5 = 625
\]

So, the common ratio of this geometric sequence is \(5\).

Would you like more details on how geometric sequences work or any other questions?

Here are some related questions to expand on the topic:
1. How do you find the sum of a geometric sequence?
2. What is the formula for the \(n\)-th term of a geometric sequence?
3. Can you derive the sum of an infinite geometric series?
4. What happens if the common ratio in a geometric sequence is less than 1?
5. How can geometric sequences be applied in real-life problems?

**Tip:** In any geometric sequence, you can find the ratio between consecutive terms by dividing any term by the previous term.

Identify the pattern in the sequence: 1, 5, 25, 125, 625.

Discover how to identify and explain the geometric sequence pattern in the numbers 1, 5, 25, 125, and 625. Understand the concept of common ratio and how it applies to geometric sequences. Suitable for Grades 7-8.

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