Page 21 - Mathematics Coursebook

2.1 Generating sequences (1)

2.1 Generating sequences (1)

3, 6, 9, 12, 15, … is a sequence of numbers.
Each number in the sequence is called a term. "e $rst term is 3, the second term is 6 and so on.
Terms that follow each other are called consecutive terms. 3 and 6 are consecutive
terms, 6 and 9 are consecutive terms and so on. Each term is 3 more than the term
before, so the term-to-term rule is: ‘Add 3.’

"ree dots written at the end of a sequence show that the sequence continues for ever. A sequence that
carries on for ever is called an infinite sequence.

If a sequence doesn’t have the three dots at the end, then it doesn’t continue for ever. "is type of
sequence is called a finite sequence.

Worked example 2.1
a Write down the term-to-term rule and the next two terms of this sequence.
2, 6, 10, 14, … , …
b The first term of a sequence is 5.
The term-to-term rule of the sequence is: ‘Multiply by 2 and then add 1.’
Write down the first three terms of the sequence.

a Term-to-term rule is: ‘Add 4.’ You can see that the terms are going up by 4 every time as
2 + 4 = 6, 6 + 4 = 10 and 10 + 4 = 14.
Next two terms are 18 and 22. You keep adding 4 to find the next two terms:
14 + 4 = 18 and 18 + 4 = 22.
b First three terms are 5, 11, 23. Write down the first term, which is 5, then use the term-to-term rule
to work out the second and third terms.
Second term = 2 × 5 + 1 = 11, third term = 11 × 2 + 1 = 23.

) Exercise 2.1

1 For each of these infinite sequences, write down:
i the term-to-term rule ii the next two terms.
a 2, 4, 6, 8, …, … b 1, 4, 7, 10, …, … c 5, 9, 13, 17, …, …
d 3, 8, 13, 18, …, … e 30, 28, 26, 24, …, … f 17, 14, 11, 8, …, …
2 Write down the first three terms of each of these sequences.

First term Term-to-term rule
a 1 Add 5

b 6 Add 8
c 20 Subtract 3
d 45 Subtract 7

e 6 Multiply by 2 and then subtract 3

f 60 Divide by 2 and then add 2

20 2 Sequences, expressions and formulae