Cambridge International Mathematics

We see that u 1 =2£ 30

u 2 =2£ 31

u 3 =2£ 32

u 4 =2£ 33 so each time the power of 3 is one less than theterm number.

So, a general formula for the sequence is un=2£ 3 n¡^1.

Example 6 Self Tutor

Find the nexttwoterms and a formula for thenth term of:

a 2 , 6 , 18 , 54 , ...... b 2 ,¡ 6 , 18 ,¡ 54 , ......^2 £(¡3)

n¡ 1

cannot be

simplified unless

we know the

value ofn.

a To get each term we multiply

the previous one by 3.

u 1 =2£ 30

u 2 =2£ 31

u 3 =2£ 32

u 4 =2£ 33

u 5 =2£ 34 = 162

u 6 =2£ 35 = 486

) un=2£ 3 n¡^1

b To get each term we multiply

the previous one by¡ 3.

u 1 =2£(¡3)^0

u 2 =2£(¡3)^1

u 3 =2£(¡3)^2

u 4 =2£(¡3)^3

u 5 =2£(¡3)^4 = 162

u 6 =2£(¡3)^5 =¡ 486

) un=2£(¡3)n¡^1

EXERCISE 26C

1 List the firstfiveterms of the geometric sequence defined by:

a un=3£ 2 n b un=3£ 2 n¡^1 c un=3£ 2 n+1

d un=5£ 2 n¡^1 e un=24£(^12 )n¡^1 f un=36£(^13 )n¡^1

g un=24£(¡2)n h un=8(¡1)n¡^1 i un=8(¡^12 )n

2 Find the nexttwoterms and a formula for thenth term of:

abc

de f

gh i

j

Example 5 Self Tutor

List the firstfiveterms of the geometric sequence defined by:

a un=5£ 2 n b un=5£ 2 n¡^1

a u 1 =5£ 21 =10

u 2 =5£ 22 =20

u 3 =5£ 23 =40

u 4 =5£ 24 =80

u 5 =5£ 25 = 160

b u 1 =5£ 20 =5

u 2 =5£ 21 =10

u 3 =5£ 22 =20

u 4 =5£ 23 =40

u 5 =5£ 24 =80

1 ,¡ 1 , 1 ,¡ 1 , 1 , ...... ¡ 1 , 1 ,¡ 1 , 1 ,¡ 1 , ...... 2 , 4 , 8 , 16 , 32 , ......

2 ,¡ 4 , 8 ,¡ 16 , 32 , ...... 6 , 18 , 54 , 162 , ...... 6 ,¡ 18 , 54 ,¡ 162 , ......

4 , 12 , 36 , 108 , ...... 2 ,¡ 14 , 98 ,¡ 686 , ...... 3 ,¡ 6 , 12 ,¡ 24 , ......

¡ 16 , 8 ,¡ 4 , 2 , ......

538 Sequences (Chapter 26)

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