Question

The product of 5 geometric means inserted between 2 and 72 is

• A. ${12}^5$
• B. ${72}^5$
• C. $2^{10}$
• D. ${12}^7$

Answer 1

The correct option is A ${12}^5$

If $G_1,G_2,G_3,........,G_n$be n geometric means inserted between two quantities a and b, then, $G_1\times G_2\times G_3\times ........\times G_n=G{}^n,\mathrm{where}G\mathrm{is}\mathrm{the}\mathrm{geometric}\mathrm{mean}\mathrm{of}a\mathrm{and}b.G_1\times G_2\times G_3\times G_4\times G_5=G^5\Rightarrow G_1\times G_2\times G_3\times G_4\times G_5={\left(\sqrt{2\times 72}\right)}^5={12}^5$