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

53

People surfing this site

Most recent posts

English Level 1
1.2 VISUAL TEXT study (AS90850) - post essays here

Posted by: CelticPineapple

11:16am 20.10.2014

English Level 2
91099 [2.1] Level 2 VISUAL text 2014 post all your Qs here

Posted by: KP11

11:53am 20.10.2014

English Level 3 & Scholarship
Scholarship English

Posted by: ravi7829

5:43pm 20.10.2014

Mathematics Level 1
EXAMS 2014 - exam format, suggested times

Posted by: mathsteacher

7:06pm 05.10.2014

Mathematics Level 2
Calculus (91262)

Posted by: mathsteacher15

3:23pm 19.10.2014

Mathematics Level 3 Calculus & Calculus Scholarship
Scholarship Calculus

Posted by: mathsteacher15

6:39am 17.10.2014

Mathematics Level 3 Statistics & Statistics Scholarship
3.14 (AS91586) Probability distributions

Posted by: mathsteacher4

6:01pm 11.10.2014

Sciences Level 1
SCIENCE 1.9 GENETIC VARIATION 90948 EXTERNAL EXAM

Posted by: hugo135

4:14pm 29.09.2014

Science Level 2 & 3
cells

Posted by: Doo

9:26pm 17.11.2013

Physics Level 2
Vote for Studyit

Posted by: mathsteacher

3:31pm 13.09.2014

Physics Level 3 & Scholarship
PHYSICS 3.6 ELECTRICAL SYSTEMS

Posted by: scienceteacher3

9:35am 17.10.2014

Biology Level 2, 3 & Scholarship
3.3 Plant & animal responses AS 91603 External

Posted by: Topper student 17

5:23pm 19.10.2014

Chemistry Level 2, 3 & Scholarship
Chem 3.5 Organic - all questions here

Posted by: Georgie_Pie

8:45pm 20.10.2014

Earth & Space Science
Where to find resources

Posted by: mathsteacher

11:13pm 14.10.2014

Other
Economics Level 2

Posted by: avartar101

6:11pm 19.10.2014