3) Determine whether each sequence is arithmetic or geometricor otherwise. If it is a geometric sequence, find the common ratio.

d) -1, 1, 4, 8, ...

Let's analyze the given sequence: \(-1, 1, 4, 8, \dots\)

### Step 1: Check for an Arithmetic Sequence
An arithmetic sequence has a common difference between consecutive terms. To find the common difference, subtract each term from the next one:
- \(1 - (-1) = 1 + 1 = 2\)
- \(4 - 1 = 3\)
- \(8 - 4 = 4\)

The differences between consecutive terms are not constant (\(2, 3, 4\)), so this is **not an arithmetic sequence**.

### Step 2: Check for a Geometric Sequence
A geometric sequence has a common ratio between consecutive terms. To find the ratio, divide each term by the previous one:
- \(\frac{1}{-1} = -1\)
- \(\frac{4}{1} = 4\)
- \(\frac{8}{4} = 2\)

The ratios between consecutive terms are not constant (\(-1, 4, 2\)), so this is **not a geometric sequence**.

### Conclusion:
The sequence \(-1, 1, 4, 8, \dots\) is neither arithmetic nor geometric.

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Would you like more details or have any other questions?

Here are 5 related questions to explore:
1. What is the definition of a harmonic sequence, and how does it differ from arithmetic and geometric sequences?
2. Can a sequence be both arithmetic and geometric? Under what conditions would that happen?
3. How can you identify whether a sequence follows a certain pattern (e.g., quadratic, cubic)?
4. What is the general form of a geometric sequence and how is it applied in solving problems?
5. How can recursive formulas be used to describe sequences?

**Tip:** If a sequence is not arithmetic or geometric, consider exploring other patterns or recursive relationships that may define the terms.

Determine whether each sequence is arithmetic or geometric or otherwise. If it is a geometric sequence, find the common ratio. Sequence: -1, 1, 4, 8, ...

Analyze the sequence -1, 1, 4, 8 to determine if it is arithmetic, geometric, or neither. This step-by-step guide covers the process of finding the common difference and common ratio, essential for understanding arithmetic and geometric sequences. Ideal for students in Grades 8-10.

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