Question

Answer the questions below. Use the Format Editor x−−√ to type math or use the Image icon to upload a photo of your work.

Is the sequence arithmetic or geometric?
Does it have a common difference or common ratio?
What is the common difference or common ratio?
What are the next three terms?
−7, −4, −1, 2, 5, . . .

Answer 1

To determine whether the given sequence \(-7, -4, -1, 2, 5, \ldots\) is arithmetic or geometric, we need to analyze the differences between the consecutive terms.

1. **Check if the sequence is arithmetic:**
- The difference between the first term and the second term:
\[
-4 - (-7) = -4 + 7 = 3
\]
- The difference between the second term and the third term:
\[
-1 - (-4) = -1 + 4 = 3
\]
- The difference between the third term and the fourth term:
\[
2 - (-1) = 2 + 1 = 3
\]
- The difference between the fourth term and the fifth term:
\[
5 - 2 = 3
\]

Since the difference between all consecutive terms is the same (3), the sequence is an **arithmetic sequence**.

2. **Common Difference:**
The common difference is \(3\).

3. **Next Three Terms:**
To find the next three terms, we can continue adding the common difference of \(3\):

- Next term after \(5\):
\[
5 + 3 = 8
\]
- Next term after \(8\):
\[
8 + 3 = 11
\]
- Next term after \(11\):
\[
11 + 3 = 14
\]

Thus, the next three terms in the sequence are \(8, 11, 14\).

### Summary:
- The sequence is arithmetic.
- It has a common difference of \(3\).
- The common difference is \(3\).
- The next three terms are \(8, 11, 14\).