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If A, G, H are the AM, GM, HM between a and b respectively then?

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If A, G, H are the AM, GM, HM between a and b respectively then?

(a) A, G, H are in hp

(b) A, G, H are in gp

(c) A, G, H are in ap

(d) None of the mentioned

I have been asked this question in examination.

This interesting question is from Harmonic Sequences in chapter Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

1 Answer

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Right option is (b) A, G, H are in gp

Best explanation: A = (a+b)/2, G = (ab)^1/2, H = 2b/(a+b), clearly AxH = G^2 thus A, G, H are in gp.

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