Q249 / 270 · NDA 2012 (Phase 2) · Mathematics

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

  • A
    $2^{n / 2}$
  • Correct answer
    B
    $2^{(n+1) / 2}$
  • C
    $2^{(n+1)}-1$
  • D
    $2^{(n-1)}$

Solution

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

Hence, the correct answer is option: 'B'.

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