# How do you find S20 for the geometric series 4 + 12 + 36 + 108 + …?

Aug 8, 2016

6973568800

#### Explanation:

Geometric series with first term $a = 4$ and common ratio $r = 3$.

Sum of geometric series given by

${S}_{n} = \frac{a \left(1 - {r}^{n}\right)}{1 - r}$

${S}_{20} = \frac{4 \left(1 - {3}^{20}\right)}{1 - 3} = 6973568800$