If a, b, c, d, e, f are in A.P. then e - c is equal to

Options

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

Answer

To solve the problem, we need to find the value of \( e - c \) given that \( a, b, c, d, e, f \) are in Arithmetic Progression (A.P.).

### Step-by-Step Solution:

1. **Understanding A.P.**:
In an arithmetic progression, the difference between consecutive terms is constant. Let's denote the first term as \( a \) and the common difference as \( d \).

2. **Expressing the terms**:
The terms of the A.P. can be expressed as:
- \( a = a \) (first term)
- \( b = a + d \) (second term)
- \( c = a + 2d \) (third term)
- \( d = a + 3d \) (fourth term)
- \( e = a + 4d \) (fifth term)
- \( f = a + 5d \) (sixth term)

3. **Finding \( e - c \)**:
Now we need to calculate \( e - c \):
\[ e - c = (a + 4d) - (a + 2d) \]

4. **Simplifying the expression**:
Simplifying the above expression:
\[ e - c = a + 4d - a - 2d \]
\[ e - c = 4d - 2d \]
\[ e - c = 2d \]

5. **Final Result**:
Therefore, \( e - c \) is equal to \( 2d \).