To find $ a_{ 10 } $ we use formula

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

In this example we have $ a_1 = 4 ~~,~~ r = \dfrac{ 1 }{ 2 } ~~\text{and}~~ n = 10 $. After substituting these values to above formula, we obtain:

$$ \begin{aligned} a_n &= a_1 \cdot r^{n-1} \\ a_{ 10 } &= 4 \cdot \left( \frac{ 1 }{ 2 } \right)^{ 10 - 1} \\ a_{ 10 } &= 4 \cdot \frac{ 1 }{ 512 } \\ a_{ 10 } &= \frac{ 1 }{ 128 } \end{aligned}$$

The first few terms of this sequence are:

$$ 4, ~~~2, ~~~1, ~~~\frac{ 1 }{ 2 } . . . $$

Geometric sequences