The list of number -10, -6, -2, 2, … is

Options

A. an AP with d = -16
B. an AP with d = 4
C. an AP with d = -4
D. not an AP

Explanation

To determine if the list of numbers -10, -6, -2, 2 is an arithmetic progression (AP), we need to find the common difference (D) between consecutive terms.

### Step-by-Step Solution:

1. **Identify the terms**:
- First term (A1) = -10
- Second term (A2) = -6
- Third term (A3) = -2
- Fourth term (A4) = 2

2. **Calculate the common difference (D)**:
- Find D by subtracting the first term from the second term:
\[ D = A2 - A1 = -6 - (-10) = -6 + 10 = 4 \]

3. **Check the next pair of terms**:
- Now, calculate the difference between the second term and the third term:
\[ D = A3 - A2 = -2 - (-6) = -2 + 6 = 4 \]

4. **Check the last pair of terms**:
- Finally, calculate the difference between the third term and the fourth term:
\[ D = A4 - A3 = 2 - (-2) = 2 + 2 = 4 \]

5. **Conclusion**:
- Since the common difference (D) is the same (4) for all pairs of consecutive terms, we can conclude that the list of numbers forms an arithmetic progression (AP) with a common difference of 4.

### Final Answer:
The list of numbers -10, -6, -2, 2 is an AP with D = 4.