To find $ a_{ 6 } $ we use formula

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

In this example we have $ a_1 = 5 ~~,~~ r = \dfrac{ 3 }{ 2 } ~~\text{and}~~ n = 6 $. After substituting these values to above formula, we obtain:

$$ \begin{aligned} a_n &= a_1 \cdot r^{n-1} \\ a_{ 6 } &= 5 \cdot \left( \frac{ 3 }{ 2 } \right)^{ 6 - 1} \\ a_{ 6 } &= 5 \cdot \frac{ 243 }{ 32 } \\ a_{ 6 } &= \frac{ 1215 }{ 32 } \end{aligned}$$

The first few terms of this sequence are:

$$ 5, ~~~\frac{ 15 }{ 2 }, ~~~\frac{ 45 }{ 4 }, ~~~\frac{ 135 }{ 8 } . . . $$

Geometric sequences