If a,b,and c are three terms of an A.P such that `a != b` then ` (b-c)/(a-b) ` may be equal to

Options

A. `sqrt(2)`
B. `sqrt(3)`
C. 1
D. 3

Answer

To solve the problem, we need to find the value of \( \frac{b - c}{a - b} \) given that \( a, b, c \) are three terms of an Arithmetic Progression (A.P.) and \( a \neq b \).

### Step-by-Step Solution:

1. **Understanding A.P. Terms**:
In an A.P., the terms can be expressed in terms of the first term and the common difference. Let:
- \( a \) be the first term,
- \( b \) be the second term, which can be expressed as \( b = a + d \),
- \( c \) be the third term, which can be expressed as \( c = a + 2d \),
where \( d \) is the common difference.

2. **Substituting the Values**:
Now, substituting \( b \) and \( c \) in the expression \( \frac{b - c}{a - b} \):
\[ b - c = (a + d) - (a + 2d) = a + d - a - 2d = d - 2d = -d \]
\[ a - b = a - (a + d) = a - a - d = -d \]

3. **Forming the Expression**:
Now, substituting these results into the expression:
\[ \frac{b - c}{a - b} = \frac{-d}{-d} = 1 \]

4. **Conclusion**:
Therefore, the value of \( \frac{b - c}{a - b} \) is equal to \( 1 \).

### Final Answer:
\[ \frac{b - c}{a - b} = 1 \]