https://file.aiquickdraw.com/mathbot/file/17268591921660s83h3p9.jpg

The sequence provided in the image is:

\[ 2, 5, 12.5, 31.25, \dots \]

### 1. Determine the type of sequence represented:
To identify the type of sequence, let's see if there is a common difference (arithmetic sequence) or a common ratio (geometric sequence).

- The ratio of the second term to the first term is:
\[
\frac{5}{2} = 2.5
\]
- The ratio of the third term to the second term is:
\[
\frac{12.5}{5} = 2.5
\]
- The ratio of the fourth term to the third term is:
\[
\frac{31.25}{12.5} = 2.5
\]

Since there is a constant ratio of 2.5 between consecutive terms, this is a **geometric sequence**.

### 2. Does the sequence have a common difference or a common ratio?
The sequence has a **common ratio**.

### 3. State the value of the common difference or common ratio:
The common ratio is \( 2.5 \).

### 4. State the next term in the sequence (do not round):
To find the next term, multiply the last term by the common ratio:
\[
31.25 \times 2.5 = 78.125
\]
Thus, the next term is **78.125**.

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Do you want more details or have any questions?

Here are 5 related questions to expand on this:
1. How do you identify whether a sequence is arithmetic or geometric?
2. What is the general formula for the \(n\)-th term of a geometric sequence?
3. How can you find the sum of the first \(n\) terms of a geometric sequence?
4. What are the key differences between arithmetic and geometric sequences?
5. How can you apply sequences in real-world problems?

**Tip:** In a geometric sequence, multiplying any term by the common ratio gives the next term, while dividing gives the previous term.

The first four terms of the sequence are 2, 5, 12.5, 31.25,... Determine the type of sequence represented. Does the sequence have a common difference or a common ratio? State the value of the common difference or common ratio. State the next term in the sequence.

Learn how to determine the common ratio in a geometric sequence with terms 2, 5, 12.5, 31.25,... and find the next term. This problem covers key concepts of geometric sequences, suitable for students in Grades 8-10.

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