Skip to content | Accessibility - list of access keys used on this site | Sitemap
Find what you need to know

Home > Subjects > Mathematics > Level 1 > 1.3 Tables, equations and graphs (AS91028) > Subject content > Linear patterns

  • Subject: Mathematics
  • AS: 91028
  • Level: 1
  • Credits: 4
  • External

Mathematics 1.3 Investigate relationships between tables, equations and graphs

Linear patterns

In a sequence of numbers, each number is called a term.
For the sequence 2, 5, 8, 11, …
The first term is 2, the second term is 5, etc.

The gap between the numbers is called the difference.
In this example the difference is 3, because 5 – 2 = 8 – 5 = 11 - 8 = 3.

Linear patterns have the same difference between the terms.
To find the rule, look for a relationship between the number of the term and the term itself. The rule is the same for each term.
In this example: 2 = 3 x 1 – 1, 5 = 3 x 2 – 1 and 8 = 3 x 3 – 1,
so the rule is t = 3 x n – 1 or t = 3n - 1

Problem

For the sequence of diagrams below, find the rule for the number of white tiles (w) in terms of the number of black tiles (b).

algebraic diagram

Answer

Number of black tiles (b) Number of white tiles (w) Difference
1 8  
3 13 5
4 18 5
4    

The difference between each term is 5. (13 - 8 = 5, 18 - 13 = 5, etc)
The difference (5) is the multiplier, so the rule must be w = 5b + ?.
To work out the ?, substitute in b = 1 and w = 8 from the first line of the table
8 = 5 x 1 + ?.
The constant term must be 3.
Giving the rule as w = 5b + 3.

For more information see:
Constructing a formula
Finding the next number in a sequence
Recognising sequences
Sequences - Finding a Rule

Back to top

0

People logged in

58

People surfing this site

Most recent posts

English Level 1
Messy handwriting

Posted by: Clarencelee

11:40pm 02.12.2015

English Level 2
91098 [2.1] Level 2 WRITTEN text post all your Qs here

Posted by: sophsta13581

5:35pm 09.06.2016

English Level 3 & Scholarship
3.1 (91472) WRITTEN TEXTS post all your essays/Qs here

Posted by: dltnals

11:41pm 09.06.2016

Mathematics Level 1
Using Studyit during the holidays

Posted by: mathsteacher

1:02pm 07.12.2015

Mathematics Level 2
Statistics (91263, 91264, 91265, 91266)

Posted by: mathsteacher15

12:55pm 24.06.2016

Mathematics Level 3 Calculus & Calculus Scholarship
Scholarship Calculus

Posted by: mathsteacher

3:17pm 18.06.2016

Mathematics Level 3 Statistics & Statistics Scholarship
Using Studyit during the holidays

Posted by: mathsteacher

1:06pm 07.12.2015

Sciences Level 1
Key to writing an E8 answer

Posted by: introvert

9:59pm 08.06.2016

Science Level 2 & 3
cells

Posted by: Doo

9:26pm 17.11.2013

Physics Level 2
FEEDBACK ON L2 PHYSICS EXAM

Posted by: paulpat99

3:25pm 22.11.2015

Physics Level 3 & Scholarship
PHYSICS 3.1 PRACTICAL INVESTIGATION

Posted by: scienceteacher3

8:24pm 14.06.2016

Biology Level 2, 3 & Scholarship
Biology Scholarship

Posted by: johnnyboy123

4:14pm 28.11.2015

Chemistry Level 2, 3 & Scholarship
CHEMISTRY SCHOLARSHIP

Posted by: Einstein

4:23pm 29.11.2015

Earth & Space Science
Where to find resources

Posted by: Josephbd

6:46pm 25.11.2015

Other
Inflation

Posted by: mathsteacher

9:23pm 07.06.2016