Q. Geometric mean of ${7,7}^{2},7^{3},\ldots 7^{n}$ is
A) $7^{\frac{n + 1}{2}}$
B) 7
C) $7^{\frac{n}{2}}$
D) $7^{n}$
Explanation
(a)
GM $= \left( {7.7}^{2}.7^{3}\ldots 7^{n} \right)^{\frac{1}{n}}$
$= ({7^{1 + 2 + 3 + \ldots + n})}^{\frac{1}{n}}$
$= \left( 7^{\frac{n(n + 1)}{2}} \right)^{\frac{1}{n}} = 7^{\left( \frac{n + 1}{2} \right)}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.