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.

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.