To find $ a_{ 6 } $ we use formula

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

In this example we have $ a_1 = 3 ~~,~~ r = -4 ~~\text{and}~~ n = 6 $. After substituting these values to above formula, we obtain:

$$ \begin{aligned} a_n &= a_1 \cdot r^{n-1} \\ a_{ 6 } &= 3 \cdot \left( -4 \right)^{ 6 - 1} \\ a_{ 6 } &= 3 \cdot \left( -1024 \right) \\ a_{ 6 } &= -3072 \end{aligned}$$

The first few terms of this sequence are:

$$ 3, ~~~-12, ~~~48, ~~~-192 . . . $$

Geometric sequences