The geometric mean of $n$ positive terms $x_1, x_2, \dots, x_n$ is equal to:

Let $S_1$ be the sum of areas of the squares whose sides are parallel to the coordinate axes. Let $S_2$ be the sum of areas of the slanted squares as shown in the figure. Then,$\frac{S_1}{S_2}$ is equal to

If $a, b, c$ are in geometric progression,then which of the following is true?

For $0 < \phi < \frac{\pi}{2}$,if $x = \sum_{n=0}^\infty \cos^{2n}\phi$,$y = \sum_{n=0}^\infty \sin^{2n}\phi$,and $z = \sum_{n=0}^\infty \cos^{2n}\phi \sin^{2n}\phi$,then:

In a $GP$ series consisting of positive terms, each term is equal to the sum of the next two terms. Then, the common ratio of this $GP$ series is

In a $G.P.$,the $3^{rd}$ term is $24$ and the $6^{th}$ term is $192$. Find the $10^{th}$ term.