If p , 1 , q are in AP and p , 2 , q are in GP, then which of the following statements is/are correct? I. p , 4 , q are in HP. II. 1 p , 1 4 , 1 q are in AP. Select the answer using the code given below.

Step-by-step solution

Since p , 1 , q are in AP, we have p + q = 2(1) = 2 . Since p , 2 , q are in GP, we have pq = 2^2 = 4 . For p , 4 , q to be in HP, the middle term must be the harmonic mean of p and q , which is given by 2pq p+q . Substituting the values of p+q and pq , we get 2(4) 2 = 4 . Thus, p , 4 , q are in HP. Statement I is correct. By the definition of harmonic progression, if p , 4 , q are in HP, their reciprocals 1 p , 1 4 , 1 q must be in AP. Thus, Statement II is also correct. Both statements I and II are correct. Answe