To find $ a_{ 9 } $ we use formula

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

In this example we have $ a_1 = -2 ~~,~~ r = -5 ~~\text{and}~~ n = 9 $. After substituting these values to above formula, we obtain:

$$ \begin{aligned} a_n &= a_1 \cdot r^{n-1} \\ a_{ 9 } &= -2 \cdot \left( -5 \right)^{ 9 - 1} \\ a_{ 9 } &= -2 \cdot \left( 390625 \right) \\ a_{ 9 } &= -781250 \end{aligned}$$

The first few terms of this sequence are:

$$ -2, ~~~10, ~~~-50, ~~~250 . . . $$

Geometric sequences