If 5th, 7th and 13th terms of an AP are in GP, then what is the ratio of its first term to its common difference?

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.

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If p times the pth term of an AP is equal to q times the qth term (p ≠ q), then what is the (p + q)th term equal to? 

Let p = ln(x), q = ln(x³) and r = ln(x⁵), where x > 1. Which of the following statements is/are correct? 

I. p, q and r are in AP.

Il. p, q and r can never be in GP.

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