find the next three terms in each sequence:   1. -8, -5,-2       2. 10, 6, 2

Let's analyze each sequence to find the pattern and determine the next three terms.

### Sequence 1: \(-8, -5, -2\)
- The difference between consecutive terms: 
  - \(-5 - (-8) = 3\)
  - \(-2 - (-5) = 3\)

Since the difference between consecutive terms is consistently \(+3\), this is an arithmetic sequence with a common difference of \(3\).

- The next term after \(-2\) is: \(-2 + 3 = 1\)
- The term after that: \(1 + 3 = 4\)
- The term after that: \(4 + 3 = 7\)

**Next three terms:** \(1, 4, 7\)

### Sequence 2: \(10, 6, 2\)
- The difference between consecutive terms:
  - \(6 - 10 = -4\)
  - \(2 - 6 = -4\)

Since the difference between consecutive terms is consistently \(-4\), this is an arithmetic sequence with a common difference of \(-4\).

- The next term after \(2\) is: \(2 - 4 = -2\)
- The term after that: \(-2 - 4 = -6\)
- The term after that: \(-6 - 4 = -10\)

**Next three terms:** \(-2, -6, -10\)

Would you like more details or have any other questions?

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**Related Questions:**

1. How do you find the nth term of an arithmetic sequence?
2. What is the sum of the first n terms of an arithmetic sequence?
3. Can you find the common difference if the first and the last term are known?
4. How does the sequence change if the common difference is negative?
5. How can arithmetic sequences be applied in real-world scenarios?

**Tip:** When analyzing sequences, always check if the differences between terms are consistent to determine if it's an arithmetic sequence.

Discover how to find the next three terms in arithmetic sequences with detailed explanations and examples. This problem covers arithmetic sequences and their application in solving sequences with constant differences. Suitable for Grades 7-9 mathematics curriculum.

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