If a, b, c, d, e, f are in AP, then `(e-c)` is equal to which one of the following?

Options

A. `2(c-a)`
B. `2(d-c)`
C. `2(f-d)`
D. `(d-c)`

Explanation

To solve the problem, we need to find the value of \( e - c \) given that \( a, b, c, d, e, f \) are in an arithmetic progression (AP).

### Step-by-Step Solution:

1. **Understanding Arithmetic Progression (AP)**:
In an arithmetic progression, the difference between consecutive terms is constant. If \( a, b, c, d, e, f \) are in AP, we can express the terms in terms of the first term \( a \) and the common difference \( d \):
- \( b = a + d \)
- \( c = a + 2d \)
- \( d = a + 3d \)
- \( e = a + 4d \)
- \( f = a + 5d \)

2. **Finding \( e - c \)**:
We need to calculate \( e - c \):
\[ e - c = (a + 4d) - (a + 2d) \]
Simplifying this gives:
\[ e - c = a + 4d - a - 2d = 4d - 2d = 2d \]

3. **Conclusion**:
Therefore, \( e - c = 2d \).

### Answer:
The value of \( e - c \) is equal to \( 2d \).