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.

Explanation

p, 1, q in AP \implies p+q=2. p, 2, q in GP \implies pq=4. HP middle term is 2pq/(p+q) = 2(4)/2 = 4, so p, 4, q are in HP (I is true). For II, 1/p + 1/q = (p+q)/(pq) = 2/4 = 1/2. The middle term is 1/4, and 2(1/4) = 1/2, so they are in AP (II is true).

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