Cambridge International Mathematics

² For thecubic sequence un=an^3 +bn^2 +cn+d, thethird differencesare constant and equal to 6 a.

The general difference table is:

n 12 3 4

un a+b+c+d 8 a+4b+2c+d 27 a+9b+3c+d 64 a+16b+4c+d

¢1 7 a+3b+c 19 a+5b+c 37 a+7b+c

¢2 12 a+2b 18 a+2b

¢3 6 a

We use the circled terms to finda,b,candd.

Example 7 Self Tutor

Find a formula for the general termunof: 6 , 13 , 20 , 27 , 34 , 41 , ......

The difference table is: n 123456

un 61320273441

¢1 77777

The¢1values are constant, so the sequence is linear.

un=an+b with a=7and a+b=6

) 7+b=6

) b=¡ 1

) the general term is un=7n¡ 1

Example 8 Self Tutor

Examine the dot sequence:

a How many dots are in the nexttwofigures?

b Find a formula forun, the number of dots in thenth figure.

a

You should not memorise

these tables but learn to

quickly generate them

when you need.

,

15 dots 21 dots

, , , , .....

Sequences (Chapter 26) 541

IGCSE01

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_26\541IGCSE01_26.CDR Tuesday, 18 November 2008 11:04:52 AM PETER