If a, b and c are in A.P than what will be their A.M ?

Options

A. 2b= a + c
B. b = a + c
C. can't be determined
D. none of these

Answer

To find the Arithmetic Mean (A.M.) of three numbers \( a, b, c \) that are in Arithmetic Progression (A.P.), we can follow these steps:

### Step-by-step Solution:

1. **Understanding A.P.**:
- If \( a, b, c \) are in A.P., then the middle term \( b \) is the average of the first and last terms \( a \) and \( c \).
- This can be expressed mathematically as:
\[ b = \frac{a + c}{2} \]

2. **Finding A.M.**:
- The Arithmetic Mean (A.M.) of any two numbers \( x \) and \( y \) is given by:
\[ \text{A.M.} = \frac{x + y}{2} \]
- In this case, we want to find the A.M. of \( a \) and \( c \):
\[ \text{A.M. of } a \text{ and } c = \frac{a + c}{2} \]

3. **Relating A.M. to A.P.**:
- Since we established that \( b = \frac{a + c}{2} \), we can see that:
\[ \text{A.M. of } a \text{ and } c = b \]
- Therefore, the A.M. of \( a \) and \( c \) is equal to \( b \).

4. **Conclusion**:
- Hence, if \( a, b, c \) are in A.P., the A.M. of \( a \) and \( c \) is simply \( b \).

### Final Answer:
The A.M. of \( a \) and \( c \) is \( b \).

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