Cambridge International Mathematics

Anumber sequenceis a set of numbers listed in a specific order, where the numbers can be found

by a specific rule.

The first term is denoted byu 1 , the second byu 2 , the third byu 3 , and so on.

Thenth termis written asun.

We often describe a number sequence in words, giving a rule which connects one term with the next.

For example, 15 , 11 , 7 , 3 ,¡ 1 , ...... can be described by the rule:

Start with 15 and each term thereafter is 4 less than the previous one.

The next two terms are u 6 =¡ 1 ¡4=¡ 5

and u 7 =¡ 5 ¡4=¡ 9 :

We say that this sequence islinearbecause each term differs from the previous one by a constant value.

Example 1 Self Tutor

Write down a rule to describe the sequence and hence find its next two terms:

a 3 , 7 , 11 , 15 , 19 , ...... b 2 , 6 , 18 , 54 , ...... c 0 , 1 , 1 , 2 , 3 , 5 , 8 , ......

a Start with 3 and each term thereafter is 4 more than the previous term.

u 6 =23and u 7 =27.

b Start with 2 and each term thereafter is 3 times the previous term.

u 5 =54£3 = 162 and u 6 = 162£3 = 486:

c The first two terms are 0 and 1 , and each term thereafter is the sum of the previous two terms.

u 8 =5+8=13and u 9 =8+13=21:

Example 2 Self Tutor

Draw the next two matchstick figures in these sequences and write the number

of matchsticks used as a number sequence:

ab

a

4 , 7 , 10 , 13 , 16 , 19 , ......

b

10 , 15 , 20 , 25 , 30 , ......

A NUMBER SEQUENCES [2.12]

, , , , ..... , , , .....

,,

534 Sequences (Chapter 26)

IGCSE01

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_26\534IGCSE01_26.CDR Monday, 27 October 2008 2:36:00 PM PETER