To find $ S_{ 5 } $ we use formula

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

In this example we have $ a_1 = 4 ~~,~~ r = 3 ~~\text{and}~~ n = 5 $. After substituting these values into the formula, we obtain:

$$ \begin{aligned} S_n &= a_1 \cdot \frac{1 - r^n}{1-r} \\ S_{ 5 } &= 4 \cdot \frac{1 - 3^{ 5 }}{1- 3 } \\ S_{ 5 } &= 4 \cdot 121 \\ S_{ 5 } &= 484 \end{aligned}$$

Geometric sequences