Write of the following are A.P.s ? If they form an A.P., find the common difference and write three more terms .
`0.2,0.22,0.222,0.2222,……`

Answer

To determine whether the given sequence \(0.2, 0.22, 0.222, 0.2222, \ldots\) 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 first term \(a_1 = 0.2\)
- The second term \(a_2 = 0.22\)
- The third term \(a_3 = 0.222\)
- The fourth term \(a_4 = 0.2222\)

2. **Calculate the difference between the first two terms**:
\[ d_1 = a_2 - a_1 = 0.22 - 0.2 = 0.02 \]

3. **Calculate the difference between the second and third terms**:
\[ d_2 = a_3 - a_2 = 0.222 - 0.22 = 0.002 \]

4. **Calculate the difference between the third and fourth terms**:
\[ d_3 = a_4 - a_3 = 0.2222 - 0.222 = 0.0002 \]

5. **Compare the differences**:
- \(d_1 = 0.02\)
- \(d_2 = 0.002\)
- \(d_3 = 0.0002\)

Since \(d_1\), \(d_2\), and \(d_3\) are not equal, the differences are not constant.

6. **Conclusion**:
Since the differences between consecutive terms are not equal, the sequence does not form an Arithmetic Progression (A.P.). Therefore, we cannot find a common difference, nor can we write three more terms in the sequence.