# Arithmetic and geometric progressions

Arithmetic and Geometric progressions.

### Arithmetic and geometric progressions

What is the difference between arithmetic progression and geometric progression or they are the same thing?

dancho

Posts: 18
Joined: Fri Mar 10, 2006 4:06 pm

They are not the same thing.

The arithmetic progression is described with $a_n=a_1 + (n-1)d$, where $d=a_{n+1}-a_n$

The geometric progression is described with $a_n=a_1*q^{n-1}$, where $q=\frac{a_{n+1}}{a_n}$

Examples:

Arithmetic: 2, 4, 6, 8, 10,... d=2

Geometric: 2, 4, 8, 16, 32,... q=2
Fed_BG

Posts: 18
Joined: Sun Jul 15, 2007 1:22 pm
Location: Bulgaria

### Re: Arithmetic and geometric progressions

The example above shows that arithmetic progression increases much slower than geometric progression.
Guest

### Re: Arithmetic and geometric progressions

Hi guys,
you may think that my question is foolish but
I do not understand the example above why d=2 and q=2 ?

Arithmetic progression: 2, 4, 6, 8, 10,... d=2
Geometric progression: 2, 4, 8, 16, 32,... q=2
Guest

### Re: Arithmetic and geometric progressions

Guest wrote:Hi guys,
you may think that my question is foolish but
I do not understand the example above why d=2 and q=2 ?

Arithmetic progression: 2, 4, 6, 8, 10,... d=2
Geometric progression: 2, 4, 8, 16, 32,... q=2

in arithmetic progression d stands for 'difference'
so you would add the value of d to the previous number in the sequence to find out the next one. that's why in
2, 4, 6, 8,.. d = 2 because it's going up by 2.

in geometric progression q, i think, stands for 'quotient'
it's similar to arithmetic progression, but instead of adding the value, you times the value of q to the previous number to find out the next number in the sequence.
therefore in the sequence: 2,4,8,16, 32 .. q = 2 because you are multiplying 2 each time
hope this helps
Guest