Arithmetic and Geometric Progression

FORMULA

Arithmetic

An arithmetic sequence is a sequence with the difference between two consecutive terms constant.   

The difference is called the common difference.

Example 01: Simple Method

3, 8, 13, 18, 23, . . .

23-18=5, 18-13=5, 13-8=5, 8-3=5

or 

3+5, 8+5, 13+5, 18+5, 23+5, 28+5, etc...

Arithmetic, the common difference d = 5

Example 02:

Using Formula

  

 

Geometric

A geometric sequence is a sequence with the ratio between two consecutive terms constant.   

This ratio is called the common ratio.

Example 01: Simple Method

1, 2, 4, 8, 16, . . . 

16/8=2, 8/4=2, 4/2=2, 2/1=2

or

1x2=2, 2x2=4, 4x2=8, 8x2=16, 16x2=32, etc....

Geometric, the common ratio r = 2  

Example 02:

Using Formula

 

Now, Let's try some exercises!

References:

http://www.scimathmn.org/stemtc/frameworks/922b-geometric-sequences-series

http://www.slideshare.net/tkjainbkn/arithmetic-geometric-and-harmonic-progression 

http://www.slideshare.net/JessicaFlint/sequences