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NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Sequences and Series

NDA 2012 · Mathematics · Sequences and Series

What is the geometric mean of the sequence 1,2,4,8 ,.........., 2^n...

What is the geometric mean of the sequence 1,2,4,81,2,4,8,.........., 2n2^n ?

Options

  1. A2n/22^{n / 2}
  2. B2(n+1)/22^{(n+1) / 2}
  3. C2(n+1)−12^{(n+1)}-1
  4. D2(n−1)2^{(n-1)}

Correct answer

B. 2(n+1)/22^{(n+1) / 2}

Step-by-step solution

We know that geometric mean of a1,a2,a3,………...ana_1, a_2, a_3, \ldots \ldots \ldots . . . a_n is \left(a_1 a_2 a_3 \ldots \ldots \ldots . . . a_n\right)^{1 / n}=2^{\frac{n(n+1)}{2} \frac{1}{n}}=2^{\frac{n+1}{2}}.
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