Find the sum of the first five term of a G.p 2,6,18 ......

The first term is $a = 2$.
The common ratio $r$ is found by dividing the second term by the first term:

$$r = \frac{6}{2} = 3$$

The sum of the first $n$ terms of a geometric progression is given by the formula:

$$S_n = \frac{a(r^n - 1)}{r - 1}$$

Here, $a=2$, $r=3$, and $n=5$.

$$S_5 = \frac{2(3^5 - 1)}{3 - 1}$$ $$S_5 = \frac{2(243 - 1)}{2}$$ $$S_5 = \frac{2(242)}{2}$$ $$S_5 = 242$$

The sum of the first five terms is:

$$242$$