Page 24 - Mathematics Coursebook

2.2 Generating sequences (2)

2 This pattern is made from squares. Pattern 1 Pattern 2 Pattern 3
a Draw the next two patterns in the sequence.
b Copy and complete the table to show the number
of squares in each pattern.

Pattern number 1 2 3 4 5

Number of squares 5 8 11

c Write down the term-to-term rule.
d How many squares will there be in: i Pattern 8 ii Pattern 10?
3 This pattern is made from blue triangles. Pattern 1 Pattern 2 Pattern 3
a Draw the next two patterns in the sequence.
b Copy and complete the table to show the number
of blue triangles in each pattern.

Pattern number 1 2 3 4 5
Number of blue triangles

c Write down the term-to-term rule.
d How many blue triangles will there be in: i Pattern 10 ii Pattern 15?

4 Jacob is using dots to draw a sequence of patterns.
He has spilled tomato sauce over the first

and third patterns in his sequence. Pattern 1 Pattern 2 Pattern 3 Pattern 4

a Draw the first and the third
patterns of Jacob’s sequence.
b How many dots will there
be in Pattern 7?
5 Harsha and Jake are looking at this sequence of patterns made from squares.
Pattern 1 Pattern 2 Pattern 3 Pattern 4

5 squares 7 squares 9 squares 11 squares

I think there are 43 squares in Pattern 20 because, if I
multiply the pattern number by 2 and add 3, I always get
the number of squares. 20 × 2 + 3 = 43.

I think there are 22 squares in Pattern 20 because the
pattern is going up by 2 each time, and 20 + 2 = 22.

Who is correct? Explain your answer.

2 Sequences, expressions and formulae 23