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Get Started Now- Lesson: 15:28
- Lesson: 24:04
- Lesson: 39:58

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.

Related Concepts: Pascal's triangle, Binomial theorem, Introduction to infinite series, Convergence & divergence of geometric series

The sum of $\, n\,$ terms of a geometric series:

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

- 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 + … . - 2.
**Geometric series formula: $s_{n}=\frac{r \cdot t_{n}-t_{1}}{r-1}$**

Determine the sum of the geometric series: 8 + 2 + $\frac{1}{2}$ + …. + $\frac{1}{{512}}$ . - 3.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?

We have over 1640 practice questions in AU Maths Extension 1 for you to master.

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