If the roots of the equation $x^3-13x^2+Kx-27=0$ are in geometric progression,then $K=$

If $a, b, c$ are the $p^{th}, q^{th}$ and $r^{th}$ terms of a $G.P.$,then $\left( \frac{c}{b} \right)^p \left( \frac{b}{a} \right)^r \left( \frac{a}{c} \right)^q$ is equal to

Write the first five terms of the sequence whose $n^{th}$ term is $a_{n} = 2^{n}$.

If $x, 2x + 2$,and $3x + 3$ are in a geometric progression,what is the fourth term?

Let $f(x)$ be a function such that $f(x+y)=f(x) \cdot f(y)$ for all $x, y \in \mathbb{N}$. If $f(1)=3$ and $\sum_{k=1}^{n} f(k)=3279$,then the value of $n$ is:

If the roots of $x^3-42x^2+336x-512=0$ are in an increasing geometric progression, then its common ratio is: (in $:1$)