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 A.P., the difference between consecutive terms is constant. Let \( x \) be the common difference.

2. **Expressing the terms**:
- The first term is \( a \).
- The second term \( b = a + x \).
- The third term \( c = a + 2x \).
- The fourth term \( d = a + 3x \).
- The fifth term \( e = a + 4x \).
- The sixth term \( f = a + 5x \).

3. **Finding \( e - c \)**:
- We have \( e = a + 4x \) and \( c = a + 2x \).
- Now, calculate \( e - c \):
\[ e - c = (a + 4x) - (a + 2x) \]
- Simplifying this expression:
\[ e - c = a + 4x - a - 2x = 4x - 2x = 2x \]

4. **Conclusion**: Therefore, \( e - c = 2x \).

### Final Answer:
\[ e - c = 2x \]

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