Question

If \( a, b, c \) are in A.P., then \( \frac{a - b}{b - c} \) is equal to:

• A. 1
• B. 2
• C. 0
• D. Undefined

Hint:

In an arithmetic progression, the common difference \( d \) is constant, so \( b - a = c - b \).

Answer 1

The Correct Option is A

We are given that \( a, b, c \) are in arithmetic progression (A.P.). In an A.P., the common difference is constant, i.e., \( b - a = c - b \). Therefore: \[ b - a = c - b \quad \Rightarrow \quad 2b = a + c. \] Now, we need to compute \( \frac{a - b}{b - c} \). Using the relationship \( b - a = c - b \), we can write: \[ \frac{a - b}{b - c} = \frac{-(b - a)}{b - c} = \frac{-(b - c)}{b - c} = -1. \] Thus, the value of \( \frac{a - b}{b - c} \) is \( 1 \).