Arithmetic and geometric progressions

[dancho]

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

[Fed_BG]

They are not the same thing.

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

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

Examples:

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

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

[Guest]

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

[Guest]

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]

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

Hi, in answer to your question,

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

[leesajohnson]

An Arithmetic progression is the sequence of numbers in which numbers such that the difference of any two successive members of the sequence is a constant.
Example: 3, 5, 7, 9.......
A Geometric progression is the sequence of number in which the next number is found the multiple of previous.
Example: 2, 6, 18......

[Guest]

Arithmetic Sequence, has a common difference (either positive or negative) between successive terms, never ends, goes to +infinity OR -infinity.
Geometric Sequence has a common ration between sucessive terms, either greater than 1 or less than 1.
If ratio is greater than 1 sequence never end goes to + or - infinity...or..diverges.
If ratio is less than 1 sequence does terminate, goes to zero...or...converges

[Guest]

Correction to last post......

Arithmetic Sequence, has a common difference (either positive or negative) between successive terms, never ends, goes to +infinity OR -infinity.

Geometric Sequence has a common ratio between sucessive terms, either positive or negative
If ratio is Greater than +1 OR Less than -1 the sequence never ends and goes to + or - infinity...so it..diverges.
If ratio is Less than +1 and Greater than -1 the sequence does terminate, goes to zero...so it...converges....-1 < r < +1