Page 219 - Math Smart - 7

Each term Is a multiple of 3.
Ti = 3 = 3 X 1
T2 = 6 = 3 X 2
Tb = 9 = 3 X 3
T4= 12 = 3 X 4
So, Tn = 3 X n.

O T25 = 3 X 25 = 75

Example 5

These patterns are made from a number of sticks.

G □□ □□□

Pattern 1 Pattern 2 Pattern 3

O Draw the next two patterns in the sequence,
o Write down the term-to-term rule.
O Write down a formula for Tp.
O Hovv many sticks are there in Pattern 75?

Solution
O The next two patterns are:
□□□□□□□CD

Pattern 4 Pattern 5
@ We can use a table to derive the term-to-term rule.

Pattern number, n 1 2 3 4 5
Number of sticks 4 7 10 13 16

The term-to-term rule is "start at 4 and add 3".
The common difference is 3, so we compare the number of sticks to multiples
of 3.
O We can find T^ by adding in the multiples of 3 and finding the difference.

Pattern number, n 1 2 3 4 5
Number of sticks 4 7 10 13 16
Multiples of 3 3 6 9 12 15

3-I-1 6 + ^ 9-t- 1 12 + 1 15 + 1
(Multiple of 3) + 1
= 4 = 1 = 10 = 13 = 16