Identify which of the following sequence is an A.P .
`5, 10 , 15, 20 ……`

Answer

To determine whether the sequence \(5, 10, 15, 20, \ldots\) is an Arithmetic Progression (A.P.), we will follow these steps:

### Step 1: Identify the terms of the sequence
The given sequence is:
- First term (\(a_1\)) = 5
- Second term (\(a_2\)) = 10
- Third term (\(a_3\)) = 15
- Fourth term (\(a_4\)) = 20

### Step 2: Calculate the differences between consecutive terms
To check if the sequence is an A.P., we need to find the difference between consecutive terms:
- Difference between the second and first term:
\[ a_2 - a_1 = 10 - 5 = 5 \]
- Difference between the third and second term:
\[ a_3 - a_2 = 15 - 10 = 5 \]
- Difference between the fourth and third term:
\[ a_4 - a_3 = 20 - 15 = 5 \]

### Step 3: Compare the differences
Now, we compare the differences we calculated:
- \(a_2 - a_1 = 5\)
- \(a_3 - a_2 = 5\)
- \(a_4 - a_3 = 5\)

All differences are equal to 5.

### Step 4: Conclusion
Since the difference between each pair of consecutive terms is the same (5), we conclude that the sequence \(5, 10, 15, 20, \ldots\) is indeed an Arithmetic Progression (A.P.).

### Final Answer
Yes, the sequence \(5, 10, 15, 20, \ldots\) is an A.P.

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