Topic 9: Sequence and Number pattern & Exercise

SEQUENCE AND NUMBER PATTERN

Introduction of sequence and number pattern
In mathematics, a sequence is an ordered list of objects. Like a set, it contains members (also called elements or terms). The number of ordered elements (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and a particular term can appear multiple times at different positions in the sequence.  

Understanding Sets

A set is a collection of objects, and it doesn't need to be a number!
This is the set of the clothes in my closet: C = {pants, t-shirt, skirt, and dress}. The capital C represents the set. So, if I said set C, we know I'm talking about clothes in my closet. The braces, { }, denote the elements, or members of the set. The elements of set C are pants, t-shirt, skirt, and dress. 

You're probably familiar with a set of real numbers: R = {…-3, -2, -1, 0, 1, 2, 3...}. The three dots indicate that the pattern continues. The elements of this group are all real numbers. So, R equals the set of real numbers.
 

A mathematical sequence is an ordered list of objects, often numbers. Sometimes the numbers in a sequence are defined in terms of a previous number in the list.

Source: Boundless. “Introduction to Sequences.” Boundless Algebra Boundless, 21 Dec. 2016. Retrieved 22 Jan. 2017 from https://www.boundless.com/algebra/textbooks/boundless-algebra-textbook/sequences-and-series-342/sequences-and-series-53/introduction-to-sequences-224-5904/

A mathematical sequence is an ordered list of objects, often numbers. Sometimes the numbers in a sequence are defined in terms of a previous number in the list.

Source: Boundless. “Introduction to Sequences.” Boundless Algebra Boundless, 21 Dec. 2016. Retrieved 22 Jan. 2017 from https://www.boundless.com/algebra/textbooks/boundless-algebra-textbook/sequences-and-series-342/sequences-and-series-53/introduction-to-sequences-224-5904/

A mathematical sequence is an ordered list of objects, often numbers. Sometimes the numbers in a sequence are defined in terms of a previous number in the list.

Source: Boundless. “Introduction to Sequences.” Boundless Algebra Boundless, 21 Dec. 2016. Retrieved 22 Jan. 2017 from https://www.boundless.com/algebra/textbooks/boundless-algebra-textbook/sequences-and-series-342/sequences-and-series-53/introduction-to-sequences-224-5904/

A mathematical sequence is an ordered list of objects, often numbers. Sometimes the numbers in a sequence are defined in terms of a previous number in the list.

Source: Boundless. “Introduction to Sequences.” Boundless Algebra Boundless, 21 Dec. 2016. Retrieved 22 Jan. 2017 from https://www.boundless.com/algebra/textbooks/boundless-algebra-textbook/sequences-and-series-342/sequences-and-series-53/introduction-to-sequences-224-5904/

A mathematical sequence is an ordered list of objects, often numbers. Sometimes the numbers in a sequence are defined in terms of a previous number in the list.

Source: Boundless. “Introduction to Sequences.” Boundless Algebra Boundless, 21 Dec. 2016. Retrieved 22 Jan. 2017 from https://www.boundless.com/algebra/textbooks/boundless-algebra-textbook/sequences-and-series-342/sequences-and-series-53/introduction-to-sequences-224-5904/

It is easiest to start by showing the growth of a simple repeating pattern.

Simple repeating pattern

Show how it grows by adding successive identical units of repeat.

Growing pattern

Counting the number of blocks give the sequence 2, 4, 6...people can see that each time a unit of repeat is added, the total number of blocks increase by 2. Also the total number is twice the number of unit of repeat.

Example 1: 

1, 4, 7, 10, 13, 16......start at 1 and jumps 3

Example 2:

1, 4, 7, 10, 13, 16, 19, 22, 25, ...

This sequence has a difference of 3 between each number.
The pattern is continued by adding 3 to the last number each time, like this:

Example 3:

3, 8, 13, 18, 23, 28, 33, 38, ...

This sequence has a difference of 5 between each number.

The pattern is continued by adding 5 to the last number each time, like this:

This video is to practice finding pattern in number. 

 

  Exercise

1) 24, 30, 36, 42

 What is the next number in the above sequence?

a) 48

b) 50

c) 24

d) 66

2) 10, 4, 2, -2.....

 What is the next number in the above sequence?

a)-6

b) -24

c) -38

d) -50  

3) What is the number before this number?
-9, -12, -15, -18..........

a) - 6
b) - 4
c)  8
d) 1