Let A1-G1 and H1 denote the arithmetic- geometric and harmonic means respectively of two distinct positive numbers- For n- 2- let An-1 and Hn-1 have arithmetic- geometric and harmonic means as An- Gn- Hn respectively-Which of the following statements is correct-

The correct option is B A_1> A_2> A_3> ...... We know A_1 gt; G_1 gt; H_1 It is given that 'A_2' is the A.M of A_1 amp; H_1 ...

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nth Term of HP

Let A1,G1 a...

Question

Let $A_{1}, G_{1}$ and $H_{1}$ denote the arithmetic, geometric and harmonic means respectively of two distinct positive numbers. For $n \geq 2$ , let $A_{n - 1}$ and $H_{n - 1}$ have arithmetic, geometric and harmonic means as $A_{n}, G_{n}, H_{n}$ respectively.
Which of the following statements is correct?

A_{1} > A_{2} > A_{3} > . . . . . .

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A_{1} < A_{2} < A_{3} < . . . . . . .

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A_{1} > A_{3} > A_{5} . . . .

and

A_{2} < A_{4} < A_{6} < . . . .

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A_{1} < A_{3} < A_{5} < . . . . .

and

A_{2} > A_{4} > A_{6} > . . . . .

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Similar questions

A_{1}, G_{1}, H_{1}

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A_{n - 1}

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A_{n}, G_{n}, H_{n}

a_{1}, a_{2}, . . . .

A_{n}, G_{n}, H_{a}

a_{1}, a_{2}, . . . ., a_{n} .

G_{1}, G_{2}, . . . ., G_{n}

A_{1}, A_{2}, . . . . ., A_{n}, H_{1}, H_{2}, . . . . ., H_{n} .

If A₁, A₂, A₃,..., A_n are n numbers between a and b, such that a, A₁, A₂, A₃,..., A_n, b are in A.P., then

A . P .

a_{1}, a_{2}, a_{3}, . . . . . ., a_{n}, . . . . .

a_{1} + a_{3} + a_{5} = - 12

a_{1} a_{2} a_{3} = 8

a_{2} + a_{4} + a_{6}

a_{1}, a_{2}, a_{3}, a_{4}, a_{5} > 0

\frac{a_{1}}{a_{2} + a_{3}} + \frac{a_{2}}{a_{3} + a_{4}} + \frac{a_{3}}{a_{4} + a_{5}} + \frac{a_{4}}{a_{5} + a_{1}} + \frac{a_{5}}{a_{1} + a_{2}} \geq \frac{5}{2}

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