Discussion

Explanation:

Consider 5 numbers p, q, r, s & t such that p, q and r are in A.P., q, r and s are in G.P. and r, s and t are in H.P. p, r and t will form a/an

Since r, s and t are in HP. let us take r = 1/1, s = 1/2 and t = 1/3
[1, 2 and 3 are in AP, hence 1/1, 1/2 and 1/3 are in HP.]

Since, q, r and s are in GP, s = 1/2 and r = 1, hence q = 2
∴ q = 2, r = 1 and s = 1/2

Since, p, q and r are in AP, r = 1 and q = 2, hence p = 3
∴ p = 3, q = 2 and r = 1

∴ p = 3, q = 2, r = 1, s = 1/2 and t = 1/3

Now, p = 3, r = 1 and t = 1/3
⇒ p, r and t form a GP.

Hence, option (b).

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