Page 23 - Mathematics Coursebook

2.2 Generating sequences (2)

2.2 Generating sequences (2)
Pattern 1 Pattern 2 Pattern 3
Here is a pattern of shapes made from dots.
"e numbers of dots used to make each pattern
form the sequence 3, 5, 7, …, …
You can see that, as you go from one pattern to the 3 dots 5 dots 7 dots
next, one extra dot is being added to each end of
the shape. So, each pattern has two more dots than Pattern 4
the pattern before. "e term-to-term rule is ‘add 2.’
"e next pattern in the sequence has 9 dots because
7 + 2 = 9.
9 dots

Worked example 2.2

Here is a pattern of triangles made from matchsticks.
Pattern 1 Pattern 2 Pattern 3

3 matchsticks 6 matchsticks 9 matchsticks
a Draw the next pattern in the sequence.
b Write down the sequence of numbers of matchsticks.
c Write down the term-to-term rule.
d Explain how the sequence is formed.

a The next pattern will have another triangle added to the end.
So pattern 4 has 12 matchsticks.

b 3, 6, 9, 12, … , … Write down the number of matchsticks for each pattern.
c Add 3 Each term is 3 more than the previous term.
d An extra triangle is added, so 3 more Describe in words how the pattern grows from one
matchsticks are added. term to the next.

) Exercise 2.2

1 This pattern is made from dots.
Pattern 1 Pattern 2 Pattern 3

a Draw the next two patterns in the sequence.
b Write down the sequence of numbers of dots.
c Write down the term-to-term rule.
d Explain how the sequence is formed.

22 2 Sequences, expressions and formulae