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The sum of first three terms of a G.P. is 13/12 and their product is – 1. Find the common ratio and the terms.
The 5th, 8th and 11th terms of a G.P. are p, q and s, respectively. Show that q2 = ps.
The sum of first three terms of a G.P. is 39/10 and their product is 1. Find the common ratio and the terms.
Show that the products of the corresponding terms of the sequences a, ar, ar2, …arn – 1 and A, AR, AR2, … ARn – 1 form a G.P, and find the common ratio.
If the pth, qth and rth terms of a G.P. are a, b and c, respectively. Prove that aq – r br – pcp – q = 1.
If the first and the nth term of a G.P. are a and b, respectively, and if P is the product of n terms, prove that P2 = (ab)n.
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