Cambridge International Mathematics

9 Consider the sequence 6 , 24 , 60 , 120 , 210 , 336 , ......

a Use the difference method to find the general term un.

b Suggest an alternative formula forunby considering u 1 =1£ 2 £ 3 ,u 2 =::::::£::::::£::::::,

u 3 =::::::£::::::£::::::, and so on.

10 Sarah has baked a cake, and wishes to divide it into pieces using straight line cuts.

Suppose un is the maximum number of pieces which can be made fromncuts, so u 1 =2,

u 2 =4, u 3 =7.

a Find un for n=4and 5.

b Use the method of differences to find a formula for un.

c If Sarah makes 10 cuts, what is the maximum number of pieces she can make?

Review set 26B

#endboxedheading

1 Write down a rule for the sequence and find its next two terms:

a 17 , 12 , 7 , 2 , ...... b ¡ 2 , 4 ,¡ 8 , 16 , ......

2

ab

3 Find the first four terms of the sequence withnth term:

a un=¡ 4 n+5 b un=(n+ 2)(n¡1)

4aFind a formula for the general term un of the sequence: 6 , 12 , 18 , 24 , ......

b Hencefind un for:

i 10 , 16 , 22 , 28 , ...... ii^57 ,^1113 ,^1719 ,^2325 , ......

c Find the 15 th term for each of the sequences inb.

5 Find un for the sequence:

a 2 , 5 , 10 , 17 , 26 , ...... b^11 ,^18 , 271 , 641 , ......

6

a un=5£ 3 n¡^1 b un=48£

¡

¡^14

¢n

7 Find un for the sequence:

a 4 ,¡ 12 , 36 ,¡ 108 , ...... b 224 , 56 , 14 , 312 , ......

1

2

1

2

3

4

1

2

3

4 5

7 6

1 cut 2 cuts 3 cuts

, , , .....

, , , .....

Draw the nexttwofigures and write down the number of dots used as a number sequence:

List the firstfourterms of the general sequence defined by:

Sequences (Chapter 26) 545

IGCSE01

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_26\545IGCSE01_26.CDR Monday, 27 October 2008 2:36:34 PM PETER