G 1 G 2 … . G n = ( 1 × 1024 ) n = 2 5 n ∴ 2 5 n = 2 45 ∴ n = 9

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MathematicsSequence & SeriesMeans / inequalityMedium2 minQB

MathematicsMediuminteger

Passage / Comprehension

Let $A_{1}, A_{2}, A_{3}, \dots, A_{m}$ be arithmetic means between –2 and 1027, and $G_{1}, G_{2}, G_{3}, \dots, G_{n}$ be geometric means between 1 and 1024. The product of the geometric means is $2^{45}$

, and the sum of the arithmetic means is

1025 \times 171

The value of $n$ is

Answer:

Solution:

$G_{1} G_{2} \dots . G_{n} = (1 \times 1024)^{n} = 2^{5 n}$

$∴ 2^{5 n} = 2^{45} ∴ n = 9$

Stream:JEESubject:MathematicsTopic:Sequence & SeriesSubtopic:Means / inequality

⏱ 2mℹ️ Source: QB

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