Write of the following are A.P.s ? If they form an A.P., find the common difference and write three more terms .
`-1.2,-3.2,-5.2,-7.2,….`

Answer

To determine if the sequence \(-1.2, -3.2, -5.2, -7.2, \ldots\) is 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 of the sequence**:
The given terms are:
- First term (\(a_1\)) = \(-1.2\)
- Second term (\(a_2\)) = \(-3.2\)
- Third term (\(a_3\)) = \(-5.2\)
- Fourth term (\(a_4\)) = \(-7.2\)

2. **Calculate the difference between the first two terms**:
\[ d_1 = a_2 - a_1 = -3.2 - (-1.2) = -3.2 + 1.2 = -2 \]

3. **Calculate the difference between the second and third terms**:
\[ d_2 = a_3 - a_2 = -5.2 - (-3.2) = -5.2 + 3.2 = -2 \]

4. **Calculate the difference between the third and fourth terms**:
\[ d_3 = a_4 - a_3 = -7.2 - (-5.2) = -7.2 + 5.2 = -2 \]

5. **Check if the differences are equal**:
Since \(d_1 = d_2 = d_3 = -2\), the sequence is indeed an A.P. with a common difference \(d = -2\).

6. **Find the next three terms**:
To find the next terms, we continue adding the common difference to the last term:
- Fifth term:
\[ a_5 = a_4 + d = -7.2 + (-2) = -9.2 \]
- Sixth term:
\[ a_6 = a_5 + d = -9.2 + (-2) = -11.2 \]
- Seventh term:
\[ a_7 = a_6 + d = -11.2 + (-2) = -13.2 \]

### Final Result:
The next three terms are \(-9.2, -11.2, -13.2\).

### Summary:
- The sequence is an A.P.
- Common difference \(d = -2\).
- Next three terms: \(-9.2, -11.2, -13.2\).