What type of arithmetic sequence is -17, -13, -9, -5

The given sequence is \(-17, -13, -9, -5\).

To determine the type of arithmetic sequence, we first need to find the common difference \(d\) between consecutive terms.

Calculating the common difference:
\[ d = -13 - (-17) = -13 + 17 = 4 \]
\[ d = -9 - (-13) = -9 + 13 = 4 \]
\[ d = -5 - (-9) = -5 + 9 = 4 \]

The common difference \(d\) is \(4\), which is positive.

An arithmetic sequence with a positive common difference is called an **increasing arithmetic sequence**.

To summarize, the given sequence \(-17, -13, -9, -5\) is an increasing arithmetic sequence with a common difference of \(4\).

If you have any further questions or need more details, please let me know! Here are 8 related questions to expand your understanding:

1. What is the 10th term of this sequence?
2. How do you find the sum of the first \(n\) terms in an arithmetic sequence?
3. What is the general formula for the \(n\)-th term of this sequence?
4. How do arithmetic sequences differ from geometric sequences?
5. What is the 20th term of this sequence?
6. How do you determine if a sequence is arithmetic?
7. What is the sum of the first 5 terms of this sequence?
8. How can we graph an arithmetic sequence?

**Tip:** Understanding the common difference in an arithmetic sequence helps in predicting the behavior of the sequence and determining any term within it using the general formula.

Learn about identifying and understanding an increasing arithmetic sequence with a detailed example. This sequence, -17, -13, -9, -5, is explored to find the common difference and categorize it accordingly. Suitable for Grades 7-9.

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