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Standard XI

Mathematics

Infinite GP

Let n ∈ N, n ...

Question

Let n $\in$ N, $n > 25$ . Let A, G, H denote the arithmetic mean. Geometric mean and harmonic mean of 25 and n. The least value of n for which A, G, H $\in$ {25, 26,...... n} is

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169

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225

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Solution

The correct option is D
225

$A = \frac{25 + n}{2}, G = 5 \sqrt{n}, H = \frac{50 n}{25 + n}$

As A, G, H are natural numbers, n must be odd pefect square. Now H will be a natural number, if n=225.(verify from options)

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Let n ∈N, n>25. Let A, G, H denote the arithmetic mean. Geometric mean and harmonic mean of 25 and n. The least value of n for which A, G, H ∈{25, 26,...... n} is

The correct option is D 225 A=25+n2,G=5√n, H=50n25+n As A, G, H are natural numbers, n must be odd pefect square. Now H will be a natural number, if n=225.(verify from options)

Let n $\in$ N, $n > 25$ . Let A, G, H denote the arithmetic mean. Geometric mean and harmonic mean of 25 and n. The least value of n for which A, G, H $\in$ {25, 26,...... n} is

The correct option is D
225

$A = \frac{25 + n}{2}, G = 5 \sqrt{n}, H = \frac{50 n}{25 + n}$

As A, G, H are natural numbers, n must be odd pefect square. Now H will be a natural number, if n=225.(verify from options)