Page 21 - Cambridge Checkpoint Mathematics Coursebook 7_Slide 02

2 Sequences, expressions and formulae

A famous mathematician called Ke
Key wordsy words
Leonardo Pisano was born around
1170, in Pisa in Italy. Later, he was Make sure you learn and
known as Fibonacci. understand these key words:
Fibonacci wrote several books. In sequence
one of them, he included a number term
pattern that he discovered in 1202. consecutive terms
Th e number pattern was named term-to-term rule
aft er him. infi nite sequence
1 1 2 3 5 8 13 21 34 … … fi nite sequence
function
Can you see the pattern? function machine
To fi nd the next number in the input
pattern, you add the previous two output
numbers. mapping diagram
So 1 + 1 = 2 Fibonacci (1170–1250). map

1 + 2 = 3 unknown
equation
2 + 3 = 5 solution
3 + 5 = 8 expression
5 + 8 = 13 and so on. variable
Th e numbers in the Fibonacci sequence are called the Fibonacci formula (formulae)
substitute
numbers. derive
Th e Fibonacci numbers oft en appear in nature. For example, the
numbers of petals on fl owers are oft en Fibonacci numbers.
Th e numbers of spirals in seed heads or pinecones are oft en Fibonacci numbers, as well.

A sunfl ower can have A pinecone can have
34 spirals turning clockwise 8 spirals turning clockwise
and 21 spirals turning and 13 spirals turning
anticlockwise. anticlockwise.
In this unit you will learn more about number patterns.

2 Sequences, expressions and formulae 19