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KCET2023MathematicsSequences and Series

If p ( 1 q + 1 r ), q ( 1 r + 1 p ), r ( 1 p + 1 q ) are in AP , then p, q, r

Options

  1. Aare in GP
  2. Bare in AP
  3. Care not in GP
  4. Dare not in AP

Correct answer

B. are in AP

Step-by-step solution

p ( 1 q + 1 r ) q ( 1 r + 1 p ) r ( 1 p + 1 q ) aligned & =p ( q+r q r ), q ( p+r p r ), r ( p+q p q ) & = p(q+r) q r +1, q(p+r) p r +1, r ( p+q p q )+1 aligned (On adding l each term) = p q+p r+q r q r , q p+q r+p r p r , r p+r q+p q p q aligned & = 1 q r , 1 p r , 1 p q in AP & = p q r q r , p q r p r , p q r p q in APs aligned (on multiply pqr both order) p, q, r also in AP.

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