Cambridge Essentials Mathematics Core 9 A4.1 Homework

/ A4.1 Homework

1 Write down the next three terms and find the term-to-term rule for generating the sequence.

a 11, 17, 23, . . . b 64, 32, 16, . . . c –10, –7, –4, . . .

d 7, 2, –3, . . . e 4, –12, 36, . . . f 0.4, 0.8, 1.2, . . .

g , , , , . . . h 1, 3, 6, 10, . . . i 3, 4, 7, 11, . . ..

2 For each part, use the position-to-term rule (t = nth term) to work out the first five terms in each sequence.

Show your working out.

a t = n + 5 b t = 4n c d t = –3n

e t = n – 0.7 f t = 3n + 2 g t = h t = 50 – 3n

3 The first five terms of some linear sequences are given. For each sequence write:

i the term-to-term rule

ii the position-to-term (nth term rule)

iii the 30th term.

a 5, 10, 15, 20, 25 b 4, 7, 10, 13, 16 c –4, –8, –12, –16, –20

d 5, 1, –3, –7, –11 e 0.3, 0.6, 0.9, 1.2, 1.5 f , , 1, ,

4 All the sequences in question 3 are linear sequences. Explain why.

5 For each sequence in question 3 state if the sequence is ascending or descending.

6 Sophie used black and white square tiles to make a sequence, arranged like this.

Pattern1 Pattern2 Pattern3

a Complete this table.

Pattern number / 1 / 2 / 3 / 4 / 5 / . . . / 20
Number of white tiles
Number of black tiles
Total number of tiles /

b Choose an expression from those in the box to represent:

i the number of white tiles in the nth pattern

ii the number of black tiles in the nth pattern

iii the total number of tiles in the nth pattern.

7 Fencing units are made of four pieces of wood.

When 2 units are put together to make a

fence they need a joining piece of wood.

This fence uses 8 pieces of wood and

1 joining piece.

a Complete:

3 fencing units → £ pieces of wood

£ joining pieces

Altogether £ pieces of wood

b Altogether how many pieces of wood are used for 5 fencing units?

c How many pieces of wood are used for n fencing units?