In the series $2,6,18,54,\dots$, what will be the $8^{\text{th}}$ term?

The given sequence is a Geometric Progression ($\text{G.P.}$) where each term is multiplied by a constant factor to get the next term.
* First term ($a$) $=2$
* Common ratio ($r$) $=\frac{6}{2}=3$

The formula for the $n^{\text{th}}$ term of a Geometric Progression is:

$$T_n=a\cdot r^{n-1}$$

For the $8^{\text{th}}$ term ($n=8$):

$$T_8=2\cdot 3^{8-1}$$

$$T_8=2\cdot 3^7$$

$$3^7=2187$$

$$T_8=2\cdot 2187=4374$$

Thus, the $8^{\text{th}}$ term is $4374$.