To find $ a_{ 8 } $ we use formula

$$ \color{blue}{a_n = a_1 \cdot r^{n-1}}$$

In this example we have $ a_1 = 3 ~~,~~ r = 2 ~~\text{and}~~ n = 8 $. After substituting these values to above formula, we obtain:

$$ \begin{aligned} a_n &= a_1 \cdot r^{n-1} \\ a_{ 8 } &= 3 \cdot 2^{ 8 - 1} \\ a_{ 8 } &= 3 \cdot 128 \\ a_{ 8 } &= 384 \end{aligned}$$

The first few terms of this sequence are:

$$ 3, ~~~6, ~~~12, ~~~24 . . . $$

Geometric sequences