Question

State whether the sequence is arithmetic, geometric or neither.
Arithmetic Geometric Neither
-8, -5, -2, 1, 4, …




243, 81, 27, 9, 3, …




-10, -20, -40, -80, -120, …




2, 3, 5, 7, 11, …




10, 14, 18, 22, 26, 30, …




6, 11, 18, 27, 38, 51, …

Answer 1

Let's analyze each sequence to determine if it is arithmetic, geometric, or neither.

1. **-8, -5, -2, 1, 4, …**
- This sequence has a common difference of 3 (e.g., -5 - (-8) = 3, -2 - (-5) = 3, and so forth).
- **Classification: Arithmetic**

2. **243, 81, 27, 9, 3, …**
- This sequence has a common ratio of 1/3 (e.g., 81/243 = 1/3, 27/81 = 1/3, etc.).
- **Classification: Geometric**

3. **-10, -20, -40, -80, -120, …**
- This sequence has a common difference of -10 (e.g., -20 - (-10) = -10, -40 - (-20) = -20, etc.).
- **Classification: Arithmetic**

4. **2, 3, 5, 7, 11, …**
- This sequence consists of prime numbers, which do not have a consistent common difference or ratio.
- **Classification: Neither**

5. **10, 14, 18, 22, 26, 30, …**
- This sequence has a common difference of 4 (e.g., 14 - 10 = 4, 18 - 14 = 4, etc.).
- **Classification: Arithmetic**

6. **6, 11, 18, 27, 38, 51, …**
- The differences in this sequence are not constant (5, 7, 9, 11, 13), so it's neither arithmetic nor geometric.
- **Classification: Neither**

### Summary:
1. Arithmetic
2. Geometric
3. Arithmetic
4. Neither
5. Arithmetic
6. Neither