The value of G 1 + G 2 + G 3 + … G n is

Since n = 9 , ∴ = ( 1024 ) 9 + 1 1 = 2 ∴ G 1 = 2 , r = 2 G 1 + G 2 + … + G n = 2 − 1 2 ⋅ ( 2 9 − 1 ) = 1024 − 2 = 1022

Mathematics - Sequence & Series Question with Solution | TestHub

MathematicsSequence & SeriesMeans / inequalityMedium2 minQB

MathematicsMediumnumerical

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 $G_{1} + G_{2} + G_{3} + \dots G_{n}$ is

Answer:

1022.00

Solution:

Since $n = 9, ∴ = (1024)^{\frac{1}{9 + 1}} = 2$

$∴ G_{1} = 2, r = 2 G_{1} + G_{2} + \dots + G_{n} = \frac{2 \cdot ( 2 ^{9} - 1 )}{2 - 1} = 1024 - 2 = 1022$

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

⏱ 2mℹ️ Source: QB

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Mathematics - Sequence & Series Question with Solution | TestHub

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JEE Advanced 2027 (Class 12+)

JEE Advanced 2027 (Class 12)