Paragraph: Let A 1 , G 1 , H 1 denote the arithmetic, geometric and harmonic means respectively, of two distinct positive numbers. For n ≥ 2 , let A n − 1 and H n − 1 has arithmetic, geometr

Question

Paragraph: Let A 1 ​ , G 1 ​ , H 1 ​ denote the arithmetic, geometric and harmonic means respectively, of two distinct positive numbers. For n ≥ 2 , let A n − 1 ​ and H n − 1 ​ has arithmetic, geometric and harmonic means as A n ​ , G n ​ , H n ​ , respectively. Question: Which one of the following statements is correct?

TestHub · Accepted Answer

A 1 ​ = 2 a + b ​ , G 1 ​ = ab ​ and H 1 ​ = a + b 2 ab ​ A n ​ = 2 A n − 1 ​ + H n − 1 ​ ​ , G n ​ H n ​ ​ = A n − 1 ​ H n − 1 ​ ​ , = A n − 1 ​ + H n − 1 ​ 2 A n − 1 ​ H n − 1 ​ ​ ​ Clearly, G 1 ​ = G 2 ​ = G 3 ​ = … = ab ​ .

Mathematics - Sequence & Series Question with Solution | TestHub

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