Write of the following are A.P.s ? If they form an A.P., find the common difference and write three more terms .
`-10,-6,-2,2,….`

Answer

To determine if the sequence -10, -6, -2, 2 forms an Arithmetic Progression (A.P.), we need to check if the difference between consecutive terms is constant.

### Step-by-Step Solution:

1. **Identify the Terms**: The given sequence is:
\[ a_1 = -10, \quad a_2 = -6, \quad a_3 = -2, \quad a_4 = 2 \]

2. **Calculate the Differences**:
- Find the difference between the first two terms:
\[ d_1 = a_2 - a_1 = -6 - (-10) = -6 + 10 = 4 \]
- Find the difference between the second and third terms:
\[ d_2 = a_3 - a_2 = -2 - (-6) = -2 + 6 = 4 \]
- Find the difference between the third and fourth terms:
\[ d_3 = a_4 - a_3 = 2 - (-2) = 2 + 2 = 4 \]

3. **Check for Common Difference**: Since \(d_1 = d_2 = d_3 = 4\), the common difference \(d\) is 4. Therefore, the sequence is an A.P.

4. **Write the Common Difference**:
\[ \text{Common Difference} = 4 \]

5. **Find the Next Three Terms**:
- To find the next term after 2, we add the common difference:
\[ a_5 = a_4 + d = 2 + 4 = 6 \]
- Next term:
\[ a_6 = a_5 + d = 6 + 4 = 10 \]
- Next term:
\[ a_7 = a_6 + d = 10 + 4 = 14 \]

6. **Final Result**: The next three terms are:
\[ 6, 10, 14 \]

### Summary:
- The sequence is an A.P.
- Common Difference: \(4\)
- Next three terms: \(6, 10, 14\)