To find $ a_{ 12 } $ we use formula

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

In this example we have $ a_1 = 1 ~~,~~ r = 3 ~~\text{and}~~ n = 12 $. After substituting these values to above formula, we obtain:

$$ \begin{aligned} a_n &= a_1 \cdot r^{n-1} \\ a_{ 12 } &= 1 \cdot 3^{ 12 - 1} \\ a_{ 12 } &= 1 \cdot 177147 \\ a_{ 12 } &= 177147 \end{aligned}$$

The first few terms of this sequence are:

$$ 1, ~~~3, ~~~9, ~~~27 . . . $$

Geometric sequences