# Geometric series

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##### Examples
###### Lessons
1. Geometric series formula:${s_n} = \frac{{{t_1}\;\left( {{r^n} - 1} \right)}}{{r - 1}}$
Determine the sum of the first twelve terms of the geometric series: 5 – 10 + 20 – 40 + … .
1. Geometric series formula: $s_{n}=\frac{r \cdot t_{n}-t_{1}}{r-1}$
Determine the sum of the geometric series: 8 + 2 + $\frac{1}{2}$ + …. + $\frac{1}{{512}}$ .
1. A tennis ball is dropped from the top of a building 15 m high. Each time the ball hits the ground, it bounces back to only 60% of its previous height. What is the total vertical distance the ball has travelled when it hits the ground for the fifth time?
###### Topic Notes
A geometric series is the sum of a finite number of terms in a geometric sequence. Just like the arithmetic series, we also have geometric series formulas to help us with that.
The sum of $\, n\,$ terms of a geometric series:

$\large S_n = \frac{t_1(r^{n}-1)} {r-1} = \frac{r \cdot t_{n} - t_{1}} {r-1}$