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Unit B3 Section 1
Simple Number Patterns

A list of numbers which form a pattern is called a sequence. In this section, straightforward sequences are continued.

Worked Examples

1

Write down the next three numbers in each sequence.

(a)

2, 4, 6, 8, 10, ...

This sequence is a list of even numbers, so the next three numbers will be

12, 14, 16.
(b)

3, 6, 9, 12, 15, ...

This sequence is made up of the multiples of 3, so the next three numbers will be

18, 21, 24.
2

Find the next two numbers in each sequence.

(a)

6, 10, 14, 18, 22, ...

For this sequence the difference between each term and the next term is 4.

Sequence6,10,14,18,22,...
Difference4444

So 4 must be added to obtain the next term in the sequence. The next two terms are

22 + 4 = 26

and

26 + 4 = 30 ,

giving

6, 10, 14, 18, 22, 26, 30, ...
(b)

3, 8, 13, 18, 23, ...

For this sequence, the difference between each term and the next is 5.

Sequence3,8,13,18,23,...
Difference5555

Adding 5 gives the next two terms as

23 + 5 = 28

and

28 + 5 = 33,

giving

3, 8, 13, 18, 23, 28, 33, ...

Exercises

Write down the next four numbers in each list.

(a)
1, 3, 5, 7, 9, , , ,
(b)
4, 8, 12, 16, 20, , , ,
(c)
5, 10, 15, 20, 25, , , ,
(d)
7, 14, 21, 28, 35, , , ,
(e)
9, 18, 27, 36, 45, , , ,
(f)
6, 12, 18, 24, 30, , , ,
(g)
10, 20, 30, 40, 50, , , ,
(h)
11, 22, 33, 44, 55, , , ,
(i)
8, 16, 24, 32, 40, , , ,
(j)
20, 40, 60, 80, 100, , , ,
(k)
15, 30, 45, 60, 75, , , ,
(l)
50, 100, 150, 200, 250, , , ,

Find the difference between terms for each sequence and hence write down the next two terms of the sequence.

(a)
5, 8, 11, 14, 17, , d:
(b)
2, 10, 18, 26, 34, , d:
(c)
7, 12, 17, 22, 27, , d:
(d)
6, 17, 28, 39, 50, , d:
(e)
8, 15, 22, 29, 36, , d:
(f)
2, 3, 3, 4, 4, , d:
(g)
4, 13, 22, 31, 40, , d:
(h)
26, 23, 20, 17, 14, , d:
(i)
20, 16, 12, 8, 4, , d:
(j)
18, 14, 10, 6, 2, , d:
(k)
11, 8, 5, 2, −1, , d:
(l)
−5, −8, −11, −14 , −17, , d:

In each part, find the answers to (i) to (iv) with a calculator and the answer to (v) without a calculator.

(a)
(i)
2 × 11 =
(ii)
22 × 11 =
(iii)
222 × 11 =
(iv)
2222 × 11 =
(v)
22222 × 11 =
(b)
(i)
99 × 11 =
(ii)
999 × 11 =
(iii)
9999 × 11 =
(iv)
99999 × 11 =
(v)
999999 × 11 =
(c)
(i)
88 × 11 =
(ii)
888 × 11 =
(iii)
8888 × 11 =
(iv)
88888 × 11 =
(v)
8888888 × 11 =
(d)
(i)
7 × 9 =
(ii)
7 × 99 =
(iii)
7 × 999 =
(iv)
7 × 9999 =
(v)
7 × 999999 =

(a)

Complete the following number pattern:

11 = 11
11 × 11 = 121
11 × 11 × 11 =
11 × 11 × 11 × 11 =
Notice: Each one is a symmetric number (these are found in Pascal's triangle).
(b)

Use your calculator to work out the next line of the pattern.

11 × 11 × 11 × 11 × 11 = 11 =
This is not a symmetric number.