Arithmetic & Geometric progression

Arithmetic&Geometric progression

 In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15 … is an arithmetic progression with common difference of 2.

If the initial term of an arithmetic progression is ${\displaystyle a_{1}}$ and the common difference of successive members is d, then the nth term of the sequence (${\displaystyle a_{n}}$) is given by:

${\displaystyle \ a_{n}=a_{1}+(n-1)d,}$

and in general

${\displaystyle \ a_{n}=a_{m}+(n-m)d.}$

A finite portion of an arithmetic progression is called a finite arithmetic progression and sometimes just called an arithmetic progression. The sum of a finite arithmetic progression is called an arithmetic series.

The behavior of the arithmetic progression depends on the common difference d. If the common difference is:

• Positive, then the members (terms) will grow towards positive infinity.
• Negative, then the members (terms) will grow towards negative infinity.

geometric progression

n.

A sequence, such as the numbers 1, 3, 9, 27, 81, in which each term is multiplied by the same factor in order to obtain the following term. Also called geometric sequence.

A sequence of numbers in which each number is multiplied by the same factor to obtain the next number in the sequence; a sequence in which the ratio of any two adjacent numbers is the same. An example is 5, 25, 125, 625, ..., where each number is multiplied by 5 to obtain the following number, and the ratio of any number to the next number is always 1 to 5. Compare arithmetic progression.

Examples

https://www.youtube.com/watch?v=gua96ju_FBk

References:

http://www.thefreedictionary.com/geometric+progression