Question

Answer the questions about the sequence below.

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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?


−8, −3, 2, 7, 12, . . .




(3 points)

Answer 1

To determine whether the sequence \(-8, -3, 2, 7, 12, \ldots\) is arithmetic or geometric, we first look at the differences between the consecutive terms.

1. **Finding the common difference:**

- From \(-8\) to \(-3\):
\[
-3 - (-8) = -3 + 8 = 5
\]

- From \(-3\) to \(2\):
\[
2 - (-3) = 2 + 3 = 5
\]

- From \(2\) to \(7\):
\[
7 - 2 = 5
\]

- From \(7\) to \(12\):
\[
12 - 7 = 5
\]

Since the difference between each pair of consecutive terms is the same (5), we can conclude that this is an **arithmetic sequence**.

2. **Common difference:**

The common difference \(d\) is \(5\).

3. **Finding the next three terms:**

- To find the next term after \(12\):
\[
12 + 5 = 17
\]

- The term after \(17\):
\[
17 + 5 = 22
\]

- The term after \(22\):
\[
22 + 5 = 27
\]

Thus, the next three terms in the sequence are \(17, 22, 27\).

**Summary:**

- The sequence is arithmetic.
- The common difference is \(5\).
- The next three terms are \(17, 22, 27\).