Page 224 - Math Smart - 7

c) Add two rows to the table as shown below to determine Ti, T2, T3, T4, T5 and T^, the
formula for finding the number of globes needed in for a sign with a height of n globes.

Pattern number 1 2 3 4 5
Height of L
Number of globes
3 5
Multiples of...
Difference between the number of globes and
the multiples of...

d) How many globes will be needed to make a sign with a height of 120 globes?

Help
• A sequence is a list of numbers that are connected by a rule, called the term-to-term rule.
Sheet
• The numbers in the sequence are called the terms of the sequence
• The general term of the sequence, T^, can be represented by an algebraic expression, for
example Tn = -2n or Tn = 3h + 1. We can use a table to find Tp.

Mathematics Connect

By studying number patterns, we become more aware of how nature works.
Amazing
Observing patterns allows us to predict the behaviour of living things and other
Mathpm;
Mathematician
phenomena. Some examples are:
• Civil engineers use their observations of traffic patterns to construct safer cities.
• Meteorologists use patterns to predict thunderstorms, tornadoes, and
hurricanes.
• Seismologists use patterns to forecast earthquakes and landslides.

One famous number sequence that occur frequently in nature and is used to
Fibonacci was born in determine the golden ratio in beautiful photos is the Fibonacci sequence. The
1170. He was an Italian Fibonacci sequence does like this: is the series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21,...
mathematician from the
We find the next term in the sequence by adding the two numbers that come
Republic of Pisa and was
before it.
considered to be "the
1
most talented Western Ti =
mathematician of the T2 = 1 + 0 =
1
Middle Ages".
T3=Ti+T2 =1+1=2
O Find the next three terms in the sequence
T4 = T2 + T3 = 1 + 2 = 3 and share your working with your partner.
T5 = T3 + T4 = 2 + 3 = 5 @ Find out how Fibonacci sequence appears in
Tg = T4 + T5 = 3 + 5 = 8 nature and where we can see it. How is the
Fibonacci sequence used in modern day?

J I Terms and Sequences