Question

If a, b, c are in AP then b-a/c-b is

Answer 1

Answer:

Step-by-step explanation:

a, b, c are in A.P, then b- a = c - b, then (b - a) / (c - b) = 1.

Answer 2

Given,

AP = a , b , c

To Find,

b-a/c-b =?

Solution,

The common difference (d) in AP is given by $a_2 -a_1$

d = b - a

$a_ 1 =a + 0d= a\\a_2 = a + 1d = b\\a_ 3 = a + 2d = c$

Putting the values of a, b, and c in (b - a) and (c - b), we get

(b - a) = a + d - (a) = d   [Equation 1]

(c - b) = a + 3d - (a + 1d) = a - a +2d - 1d

(c - b) = d  [Equation 2]

We have to find ratio  of b-a/c-b

Therefore, putting values from equation 1 and 2

Ratio = (b - a)/(c - b) = d / d

Ratio = 1

Hence, if a, b, c are in AP then b-a/c-b is 1.