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.

---

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.