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The G. M. of the numbers 3, 32, 33, ..... 3n is :

This question was previously asked in
OPSC ASO (Paper II) Previous Year Paper 2018
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  1. 32/n
  2. \(3^{\frac{n−1}{2}}\)
  3. \(3^{\frac{n}{2}}\)
  4. \(3^\frac{n+1}{2}\)

Answer (Detailed Solution Below)

Option 4 : \(3^\frac{n+1}{2}\)
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Detailed Solution

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Solution:

G.M. = (3 × 32 × 33 .........3n)1/n

⇒ G.M. = 3(1 + 2 + 3 + 4 ....... n)/n

⇒ G.M. = 3n(n + 1)/2n

∵​ G.M. = 3(n + 1)/2

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