Geometric series - Sequences and Series

Geometric series

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.

Basic Concepts
Arithmetic series
Geometric sequences

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

Lessons

Notes:

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

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

Geometric series

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Notes:

The sum of n \, n\, n terms of a geometric series: Sn=t1(rn−1)r−1=r⋅tn−t1r−1\large S_n = \frac{t_1(r^{n}-1)} {r-1} = \frac{r \cdot t_{n} - t_{1}} {r-1} Sn​=r−1t1​(rn−1)​=r−1r⋅tn​−t1​​

1.

Geometric series formula:sn=t1(rn−1)r−1{s_n} = \frac{{{t_1}\;\left( {{r^n} - 1} \right)}}{{r - 1}}sn​=r−1t1​(rn−1)​ Determine the sum of the first twelve terms of the geometric series: 5 – 10 + 20 – 40 + … .

2.

Geometric series formula: sn=r⋅tn−t1r−1s_{n}=\frac{r \cdot t_{n}-t_{1}}{r-1}sn​=r−1r⋅tn​−t1​​ Determine the sum of the geometric series: 8 + 2 + 12\frac{1}{2}21​ + …. + 1512\frac{1}{{512}}5121​ .

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?

Geometric series

Don't just watch, practice makes perfect.

We have over 1850 practice questions in Algebra for you to master.

Algebra
Arithmetic series

Algebra
Geometric sequences

or

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

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

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 + … .

Geometric series formula: $s_{n}=\frac{r \cdot t_{n}-t_{1}}{r-1}$
Determine the sum of the geometric series: 8 + 2 + $\frac{1}{2}$ + …. + $\frac{1}{{512}}$ .