Cambridge International Mathematics

ANSWERS 735

eStart with 162 and then multiply each successive term by^13 :

2 ,^23.

fStart with 405 and then multiply each successive term by^13 :

5 , 123.

3a 25 , 36 b 36 , 49 c 125 , 216 d 361 , 491

e 16 , 22 f 42 , 56

4aThe first two terms are 1 and 1 and from then on the next

term is the sum of the previous two terms: 13 , 21.

bThe first two terms are 1 and 3 and from then on the next

term is the sum of the previous two terms: 18 , 29.

cEach term is made up by adding two successive prime num-

bers starting 2+3, 3+5,5+7, etc.: 36 , 42.

5a

3 , 6 , 9 , 12 , 15 , ......

b

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

c

4 , 13 , 26 , 43 , 64 , ......

d

5 , 12 , 19 , 26 , 33 , ......

e

6 , 11 , 16 , 21 , 26 , ......

f

4 , 16 , 36 , 64 , 100 , ......

6a

1 , 3 , 6 , 10 , 15 , 21 , ......

b

1 , 4 , 9 , 16 , 25 , 36 , ......

c

1 , 4 , 9 , 16 , 25 , ......

d

2 , 8 , 18 , 32 , 50 , ......

EXERCISE 26B

1a 5 , 7 , 9 , 11 , ...... b 7 , 9 , 11 , 13 , ......

c 5 , 8 , 11 , 14 , ...... d 8 , 11 , 14 , 17 , ......

e¡ 1 ,¡ 3 ,¡ 5 ,¡ 7 , ...... f 1 ,¡ 1 ,¡ 3 ,¡ 5 , ......

g 3 , 0 ,¡ 3 ,¡ 6 , ...... h 13 , 9 , 5 , 1 , .......

i 69 , 62 , 55 , 48 , ......

2a 2 , 5 , 10 , 17 , ...... b 0 , 3 , 8 , 15 , ......

c 2 , 6 , 12 , 20 , ...... d 3 , 8 , 15 , 24 , ......

e 2 , 9 , 28 , 65 , ...... f 2 , 15 , 44 , 95 , ......

3aun=2n biun=2n+2 iiun=2n¡ 1

4aun=5n biun=5n+1 iiun=5n¡ 2

5aun=2n bun=3£ 2 n

6aun=n

biun=n+1 iiun=n+2 iiiun=

1

n

iv un=

1

n+1

vun=

n

n+1

vi un=

n+2

n

vii un=n(n+1) viiiun=(n+ 1)(n+2)

ix un=n(n+2) x un=

3 n¡ 2

3 n

7aun=n^2

biun=(n+1)^2 iiun=n^2 ¡ 1

iii un=^1

n^2

iv un= n

(n+1)^2

8aun=n^3 b un=n^3 ¡ 1

cun=3£ 2 n¡^1 d un=24£(^12 )n¡^1

EXERCISE 26C

1a 6 , 12 , 24 , 48 , 96 , ...... b 3 , 6 , 12 , 24 , 48 , ......

c 12 , 24 , 48 , 96 , 192 , ...... d 5 , 10 , 20 , 40 , 80 , ......

e 24 , 12 , 6 , 3 , 112 , ...... f 36 , 12 , 4 , 113 ,^49 , ......

g¡ 48 , 96 ,¡ 192 , 384 ,¡ 786 , ......

h 8 ,¡ 8 , 8 ,¡ 8 , 8 , ...... i ¡ 4 , 2 ,¡ 1 ,^12 ,¡^14 , ......

2a¡ 1 , 1 ; un=(¡1)n¡^1 orun=(¡1)n+1

b 1 ,¡ 1 ; un=(¡1)n c 64 , 128 ; un=2n

d¡ 64 , 128 ; un=2£(¡2)n¡^1

e 486 , 1458 ; un=6£ 3 n¡^1

f 486 ,¡ 1458 ; un=6£(¡3)n¡^1

g 324 , 972 ; un=4£ 3 n¡^1

h 4802 ,¡33 614; ub=2£(¡7)n¡^1

i 48 ,¡ 96 ; un=3£(¡2)n¡^1

j ¡ 1 ,^12 ; un=¡ 16 £(¡^12 )n¡^1

EXERCISE 26D

1aun=4n¡ 3 bun=20¡ 3 n c un=n^2 +n

dun=n^2 +3n¡ 4 eun=n^3 +5

fun=^12 n^3 +^32 n or un=

n(n^2 +3)

2

2aun=4n^2 ¡ 2 n

bu 1 =1£ 2 , u 2 =3£ 4 , u 3 =5£ 6 , u 4 =7£ 8 ,

etc

) un=(2n¡1)£ 2 n

3au 1 =2, u 2 =8, u 3 =18, u 4 =32, u 5 =50,

u 6 =72, u 7 =98

bun=2n^2 c u 30 = 1800dots

4a

bun=^12 n^2 +^12 n or un=

n(n+1)

2

c 15 931handshakes

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(15) (21)

(28)

A

BC

D

FE FE

AC

G D

B

AE

B D

H F

G

C

IB MYP_3 ANS

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