Is the sequence 12, 8,4,0…………. An A.P.? If yes, state is first term and common differnce.

Answer

To determine if the sequence 12, 8, 4, 0 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 (A1) = 12
- Second term (A2) = 8
- Third term (A3) = 4
- Fourth term (A4) = 0

### Step 2: Calculate the common difference
To check if the sequence is an A.P., we need to find the common difference (d) between consecutive terms. The common difference is calculated as follows:
- d = A2 - A1 = 8 - 12 = -4
- d = A3 - A2 = 4 - 8 = -4
- d = A4 - A3 = 0 - 4 = -4

### Step 3: Compare the common differences
Now, we compare the common differences we calculated:
- d1 = -4
- d2 = -4
- d3 = -4

Since all the common differences are equal, we can conclude that the sequence is indeed an A.P.

### Step 4: State the first term and common difference
- The first term (A1) of the A.P. is 12.
- The common difference (d) is -4.

### Final Answer
Yes, the sequence 12, 8, 4, 0 is an A.P. The first term is 12, and the common difference is -4.

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