Page 218 - Math Smart - 7

9.2.3 Number seauences in
geometrical patterns

Geometrical or spatial patterns are number patterns represented by diagrams.
Recording the numbers in a table helps us spot the pattern and describe the
general rule for the pattern.

-• Think and Share

6 people can sit around one rectangular table
as shown.

If 10 tables are put together so that they join
at their breadths one after another, how many
people can sit around these 10 tables?
Try drawing a diagram to find out. Can you
spot a pattern? Can you write a formula to
represent the general term, 1^?

Example 4

These patterns of hexagons form a sequence.

t tt ttt tttt

Pattern 1 Pattern 2 Pattern 3 Pattern 4

O Write down the term-to-term rule.
@ Find a formula Tn for Pattern n.
O How many hexagons will be in Pattern 25?

Solution
The number of hexagons in each pattern form the sequence 3, 6, 9, 12, ...

O The term-to-term rule is "add 3 hexagons to each pattern to get the next
pattern". The common difference is 3.
@ Use a table to find Tn-

Pattern number, n 1 2 3 4
3 6 9 12
Number of hexagons
= 3x1 = 3X2 = 3X3 = 3X4

Terms and Sequences