Identify which of the following sequence is an A.P .
5,5,5,5,5,`……`

Answer

To determine if the sequence 5, 5, 5, 5, 5, ... 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**: The sequence given is 5, 5, 5, 5, 5, ...

2. **Calculate the Differences**:
- The first term (a1) = 5
- The second term (a2) = 5
- The difference between the first and second term:
\[ a2 - a1 = 5 - 5 = 0 \]
- The third term (a3) = 5
- The difference between the second and third term:
\[ a3 - a2 = 5 - 5 = 0 \]
- The fourth term (a4) = 5
- The difference between the third and fourth term:
\[ a4 - a3 = 5 - 5 = 0 \]

3. **Check Consistency of Differences**:
- The differences calculated are:
- Between a1 and a2: 0
- Between a2 and a3: 0
- Between a3 and a4: 0
- All differences are equal to 0.

4. **Conclusion**: Since the difference between each consecutive term is the same (0), we can conclude that the sequence is an arithmetic progression (A.P.).

### Final Answer:
The sequence 5, 5, 5, 5, ... is an arithmetic progression (A.P.).

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