Which one is A.P. series ?

Options

A. `2,4,8,12,……..`
B. `0.2, 0.22, 0.222,……….`
C. `-10, -6, -2, 2,…….`
D. `1, 3,9.27`……..

Answer

To determine which of the given sequences 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 Options**: We have four sequences to check:
- Option 1: 2, 4, 8, 12
- Option 2: 0.2, 0.22, 0.222
- Option 3: -10, -6, -2, 2
- Option 4: 1, 3, 9, 9.27

2. **Check Option 1**:
- Calculate the differences:
- 4 - 2 = 2
- 8 - 4 = 4
- 12 - 8 = 4
- Since the differences are not constant (2, 4, 4), this is **not an A.P.**.

3. **Check Option 2**:
- Calculate the differences:
- 0.22 - 0.2 = 0.02
- 0.222 - 0.22 = 0.002
- Since the differences are not constant (0.02, 0.002), this is **not an A.P.**.

4. **Check Option 3**:
- Calculate the differences:
- -6 - (-10) = 4
- -2 - (-6) = 4
- 2 - (-2) = 4
- Since the differences are constant (4, 4, 4), this is an **A.P.**.

5. **Check Option 4**:
- Calculate the differences:
- 3 - 1 = 2
- 9 - 3 = 6
- 9.27 - 9 = 0.27
- Since the differences are not constant (2, 6, 0.27), this is **not an A.P.**.

6. **Conclusion**: The only sequence that is an A.P. is **Option 3: -10, -6, -2, 2**.