To find $ a_{ 7 } $ we use formula

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

In this example we have $ a_1 = 1 ~~,~~ r = -\dfrac{ 2 }{ 3 } ~~\text{and}~~ n = 7 $. After substituting these values to above formula, we obtain:

$$ \begin{aligned} a_n &= a_1 \cdot r^{n-1} \\ a_{ 7 } &= 1 \cdot \left( -\frac{ 2 }{ 3 } \right)^{ 7 - 1} \\ a_{ 7 } &= 1 \cdot \left( \frac{ 64 }{ 729 } \right) \\ a_{ 7 } &= \frac{ 64 }{ 729 } \end{aligned}$$

The first few terms of this sequence are:

$$ 1, ~~~-\frac{ 2 }{ 3 }, ~~~\frac{ 4 }{ 9 }, ~~~-\frac{ 8 }{ 27 } . . . $$

Geometric sequences