Question

prove that if a, b, c are in HP, if a/c=a-b/b-c​

Answer 1

Answer:

a, b, c are in HP

so 1/a, 1/b, 1/c are in AP.

thus 1/b – 1/a = 1/c – 1/b

=> (a – b) / ab = (b – c) / bc

=> (a – b) / (b – c) = ab / bc

=> (a – b) / (b – c) = a / c