Question

Insert $5G.Ms$ between $1/3$ and $9$ and verify that their product is the $5th$ power of the $G.M.$ between $1/3$ and $9$

Answer 1

$5$ G.M.'s are inserted between $\frac{1}{3}and9$

$\frac{1}{3}.r^6=9r^6=27r=\sqrt{3}$

Product of all G.M.'s$={\left(\frac{1}{3}\right)}^5\left(r^{15}\right)=9\sqrt{3}$

G.M of $\frac{1}{3}and9=\sqrt{3}$

$(\sqrt{3}{)}^m=9\sqrt{3}m=5$

Product of inserted G.M $=5^{th}$ power of G.M of $\frac{1}{3}and9$