If A, B, C are p t h , q t h and r t h terms of a GP respectively then A q - r . B r - p . C p - q = ….

Step-by-step solution

Let first term and common ratio of a GP are m and n respectively. Then, A = m n p - 1 … (i) B = m n q - 1 … (ii) and C = m n r - 1 … (iii) Now, A q - r . B r - p . C p - q = m q - r . n q - r p - 1 . m r - p . n r - p q - 1 . m p - q . n p - q r - 1 = m q - r + r - p + p - q . n q p - q - r p + r + r q - r - r - p q + p + p r - p - q r + q = m 0 . n 0 = 1 × 1 = 1