## Question

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

### Solution

Correct option is

225

As A, G, H are natural numbers, n must odd be perfect square. Now, will be a natural number if we take n = 225.

#### SIMILAR QUESTIONS

Q1

easy
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Q2

easy
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Q3

easy
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Q4

medium
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Q5

Given a sequence of four numbers such that the first three are in G.P. and the last three are in A.P. with common difference 6. If the first and the fourth numbers are equals, then common ratio of the G.P. is

easy
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Q6

easy
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Q7

easy
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Q8

If a, b, c are three distinct numbers such that a, b, c are in A.P. and a, c – b, b – a are in G.P. then the ratio a : b : c equals

easy
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Q9

easy
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Q10

easy
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