write three examples of geometric sequence with a common ratio of 1

A geometric sequence with a common ratio of 1 means that each term in the sequence is the same as the previous term. Here are three examples:

1. **Example 1**: \(2, 2, 2, 2, 2, \dots\)
   - Common ratio (\(r\)) = 1
   - Each term is the same as the previous one, so the sequence remains constant.

2. **Example 2**: \(-5, -5, -5, -5, -5, \dots\)
   - Common ratio (\(r\)) = 1
   - Each term is multiplied by 1, so the sequence doesn't change.

3. **Example 3**: \(7, 7, 7, 7, 7, \dots\)
   - Common ratio (\(r\)) = 1
   - The sequence remains constant with each term equal to 7.

Would you like more details on geometric sequences or have any questions?

Here are 5 related questions:
1. What is the general formula for a geometric sequence?
2. How does the common ratio affect the growth or decay of a geometric sequence?
3. What happens to a geometric sequence if the common ratio is negative?
4. How do you find the sum of the first \(n\) terms in a geometric sequence?
5. Can a geometric sequence have a common ratio of 0?

**Tip**: In a geometric sequence, when the common ratio is 1, the sequence doesn't change and remains constant for all terms.

Explore three examples of geometric sequences where each term is the same as the previous one, demonstrating a common ratio of 1. Understand the properties of geometric sequences and their constant nature. Suitable for Grades 7-9 students studying arithmetic sequences and series.

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