Question

If a, b, c are in AP or GP HP, then (a - b)/(b - c) is equal to

a. b/a or 1 or b/c

b. c/a or c/b or 1

c. 1 or a/b or a/c

d. 1 or a/b or c/a

Answer 1

Correct option c. 1 or a/b or a/c

Explanation:

a, b, c ∈ A.P ⇒ a - b = b - c ⇒ (a - b)/(b - c) = 1

a, b, c ∈ G.P ⇒ a/b = b/c = (a - b)/(b - c)

a, b, c ∈ H.P ⇒ b = ac/(a + c) ⇒ ab + bc = ac

⇒ ab - ac = ac - bc

⇒ (a - b)/(b - c) = a/c