Question

The product of 6 geometric means between 8 and $\frac{1}{16}$ will be:

• A. $1/16$
• B. $1/8$
• C. $1/2$
• D. $1/4$

Answer 1

Answer: (B)

There are 6 G.M.s between 8 and $\frac{1}{16}$
$\therefore 8,G_1,G_2,\dots \dots ,G_6,\frac{1}{16}$ are in G.P.
we know that product of $n$ G.M. between two numbers is $n^{\text{th }}$ power of single G.M. between two numbers.
G.M. of 8 and $\frac{1}{16}$ is $\sqrt{8\cdot \frac{1}{16}}=\frac{1}{\sqrt{2}}$
$\therefore$ product of 6 G.Ms $={\left(\frac{1}{\sqrt{2}}\right)}^6=\frac{1}{8}$