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

305

People surfing this site

Most recent posts

English Level 1
Please read this BEFORE posting on Level 1 English

Posted by: DonaldMills

5:24pm 21.11.2016

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

Posted by: Jujuju279

9:19pm 21.11.2016

English Level 3 & Scholarship
3.2 (91473) VISUAL TEXTS post all your essays/Qs here

Posted by: pinkfluffybunnies

11:15am 22.11.2016

Mathematics Level 1
LEVEL 1 MATHS EXAM COMMENTS - How did it go?

Posted by: ben8661

6:23pm 18.11.2016

Mathematics Level 2
LEVEL 2 MATHS EXAM COMMENTS - How did it go?

Posted by: mathsteacher

12:06pm 25.11.2016

Mathematics Level 3 Calculus & Calculus Scholarship
3.3 (AS91575) Trigonometry

Posted by: mathsteacher

11:10pm 01.12.2016

Mathematics Level 3 Statistics & Statistics Scholarship
2016 Statistics Exam - How did it go?

Posted by: mathsteacher

12:14pm 25.11.2016

Sciences Level 1
Level One Science - Chemical Reactions 1.5

Posted by: ashboxcalculations

10:51pm 30.11.2016

Physics Level 2
2016 EXAM DISCUSSION

Posted by: artechica

4:12pm 15.11.2016

Physics Level 3 & Scholarship
2016 EXAM FEEDBACK

Posted by: ragdoll

4:59pm 16.11.2016

Biology Level 2, 3 & Scholarship
Scholarship Biology 2016

Posted by: Be27

10:16am 20.11.2016

Chemistry Level 2, 3 & Scholarship
2016 chem papers how did they go

Posted by: dydxx

8:46am 22.11.2016

Earth & Space Science
Where to find resources

Posted by: Josephbd

6:46pm 25.11.2015

Other
Media Schol Essay Feedback

Posted by: weirdonumber1

6:38pm 26.11.2016