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  • Confused! kindly explain, The GM of the series 1, 2, 4, 8, 16, ….. 2n is

The GM of the series 1, 2, 4, 8, 16, ….. 2n is

  • Option 1)

    2^{n+\frac{1}{2}}

  • Option 2)

    2^{n-\frac{1}{2}}

  • Option 3)

    2^{n+\frac{3}{2}}

  • Option 4)

    2^{n/{2}}

 

Answers (1)

best_answer

As we learned

Geometric Mean -

In case of discrete data 

G= e^{\frac{1}{n}}\sum_{i=1}^{n}\log_{e}\left ( n_{i} \right )

-

 

 We can solve it without using Logarithm as well.

 

GM=n\sqrt{1.2.3.4.8.16.......2^n}

           =\sqrt{2^1.2^2.2^3.2^4......2^n}

             =\left ( 2^{1+2+3+4......+n} \right )^{1/n}

              =\left ( 2^{n(n+1)/2} \right )^{1/n}

              =\left ( 2^{n+1/2} \right )


Option 1)

2^{n+\frac{1}{2}}

Option 2)

2^{n-\frac{1}{2}}

Option 3)

2^{n+\frac{3}{2}}

Option 4)

2^{n/{2}}

Posted by

Himanshu

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