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:
${s_n} = \frac{{{t_1}\;\left( {{r^n} - 1} \right)}}{{r - 1}}$
$=\frac{r \cdot t_{n}-t_{1}}{r-1}$

Geometric series

Don't just watch, practice makes perfect.

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

Get Started Now

Try reviewing these fundamentals first

AlgebraArithmetic series

AlgebraGeometric sequences

Nope, got it.

Play next lesson

Nope, got it.

Play next lesson

That's it, no more lessons

Goto next topic

Still don't get it?

Nope, I got it.

Still don't get it?

Review these basic concepts…

Arithmetic series

Geometric sequences

Nope, I got it.

Play next lesson or Practice this topic

Start now and get better math marks!

Keep exploring StudyPug

Start now and get better math marks!

Keep exploring StudyPug

Lesson: 1

Selected

Lesson: 2

Lesson: 3

Intro

Learn

Practice

Do better in math today

Don't just watch, practice makes perfect.

Do better in math today

Don't just watch, practice makes perfect.

Lessons

Notes:

• the sum of n terms of a geometric series: sn=t1(rn−1)r−1{s_n} = \frac{{{t_1}\;\left( {{r^n} - 1} \right)}}{{r - 1}}sn​=r−1t1​(rn−1)​ =r⋅tn−t1r−1=\frac{r \cdot t_{n}-t_{1}}{r-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:
${s_n} = \frac{{{t_1}\;\left( {{r^n} - 1} \right)}}{{r - 1}}$
$=\frac{r \cdot t_{n}-t_{1}}{r-1}$

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 + $\frac{1}{2}$ + …. + $\frac{1}{{512}}$ .