Page 16 - Cambridge+Checkpoint+Mathematics+Coursebook+9

2 Sequences and functions

All children learn to count. !ey learn this sequence of numbers. Key words
1 2 3 4 5 6 7 8 9 10 11 12 13 . . . . . Make sure you learn and
You can use this sequence to make a new sequence by colouring understand these key words:
numbers in equal steps. linear sequence
Here are three examples: non-linear sequence
1 2 3 4 5 6 7 8 9 10 11 12 13 . . . . . term-to-term rule

!is gives the odd numbers position-to-term rule
1 3 5 7 9 11 13 15 17 . . . . . arithmetic sequence
nth term
1 2 3 4 5 6 7 8 9 10 11 12 13 . . . . . inverse function

!is gives the sequence

2 5 8 11 14 17 20 23 . . . . .

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 . . . . .
!is gives the sequence

2 7 12 17 22 27 32 . . . . .

Can you "nd the 10th term of each sequence?

You should know how to use a formula for the nth term of a sequence.
Here are the nth terms of the three sequences. !ey are not in the correct order:

3n – 1 5n – 3 2n – 1
Which nth term goes with which sequence?

If you have a formula for the nth term it is easy to "nd the 10th term
of the sequence. Check that you found the 10th term of each of the
sequences above correctly.

Using formulas like this is an example of algebra.

!e word algebra comes from the title of a book written by the
Persian mathematician Muhammad ibn Mūsā al-Khwārizmī
in 820 CE. !e book was called Hisab al-jabr w’al-muqabala.

Can you see a word in the title that looks similar to the word

algebra? !is was the "rst book ever written about algebra.

Al-Khwārizmī

In this chapter you will be studying di&erent sequences and "nding a formula for the nth term for some

of them.
2 Sequences and functions 15