if 1/a,1/b,1/c are in a.p .prove that a/c=(a-b)/(b-c).

if these are in an AP then there would be a common difference (d)

so to find the (d):-

a₂ - a₁ = a₃ - a₂

1/b - 1/a = 1/c - 1/b

(a - b)/ab = (b - c)/bc

cross multiplying.....

(a - b)/(b - c) = ab/bc

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

here is ur anwer....