The sum of the first k terms of a series S is $3k{}^2+5k$. Which one of the following is correct?

The sum of the first 8 terms of a GP is five times the sum of its first 4 terms. If $r$≠$1$ is the common ratio, then what is the number of possible real values of r?

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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