By studying patterns in math, humans become aware of patterns in our world. Observing patterns allows individuals to develop their ability to predict future behavior of natural organisms and phenomena. Civil engineers can use their observations of traffic patterns to construct safer cities. Meteorologists use patterns to predict thunderstorms, tornadoes, and hurricanes. Seismologists use patterns to forecast earthquakes and landslides. Mathematical patterns are useful in all areas of science. The history of mathematics is a history of people fascinated by numbers. A driving force in mathematical development has always been the need to solve practical problems. However, man's innate curiosity and love of pattern has probably had an equal part in its development. The Pythagoreans (circa 6th century BC) were a secret society who considered numbers sacred and tried to find relations between numbers and nature. For example, they developed the musical scales as number ratios. They discovered that 6 and 28 are the first two 'perfect' numbers (a number equal to the sum of it's proper divisors. )They also knew that squared numbers are the sums of sequences of consecutive odd numbers. |

A sequence is a pattern of numbers that are formed in accordance with a definite rule.We can often describe number patterns in more than one way. To illustrate this, consider the following sequence of numbers {1, 3, 5, 7, 9, …}.Clearly, the first term of this number pattern is 1; and the terms after the first term are obtained by adding 2 to the previous term. We can also describe this number pattern as a set of odd numbers.|

Number patterns

There is varies types of number pattern that we can found in the world. However, the most common types of number patterns is Arithmetics Sequence and Geometric Sequence. * Arithmetics Sequence

An Arithmetic Sequence is made by adding some value each time.

Example 1:

T1

T2

T3

T4

T5

T6

T7

T8

1| 3| 5| 7| 9| 11| 13| 15|

+2

+2

+2

+2

+2

+2

+2

This sequence has a difference of 2 between each number.The pattern is continued by adding 2 to the last number each time. The value adding for each time is called as “common difference”. Therefore ,2 is the common difference for this arithmetics sequence.

Example 2 :

T1

T2

T3

T4

T5

T6

T7

T8

0| 5| 15| 20| 25| 30| 35| 40|

+5

+5

+5

+5

+5

+5

+5

This sequence has a difference of 5 between each number.The pattern is continued by adding 5 to the last number each time. The value adding for each time is called as “common difference”. Therefore ,5 is the common difference for this arithmetics sequence.

Example 3:

The common difference also can be negative.

T1

T2

T3

T4

T5

T6

T7

T8

26| 23| 20| 17| 14| 11| 8| 5|

-3

-3

-3

-3

-3

-3

-3

The common difference is -3. The pattern is continued by subtracting 3 each time. This sequence has a difference of -3 between each number.

* Geometric sequence

A Geometric Sequence is made by multiplying some value each time.

Example 1:

T2

T1

T3

T4

T5

T6

T7

T8

4| 16| 64| 256| 1024| 4096| 16384| 65536|

x4

x4

x4

x4

x4

x4

x4

This sequence has a factor of 4 between each number. The pattern is continued by multiplying by 4 each time....