Block 1

Sequences

What is to be learned?

• How to find the formula for a sequence• How to generate a sequence, given the

formula

Sequence

3 5 7 9 11 , , , , , ….

1st term 2nd term

Term Number 1 2 3 4 5 n

any term? nth term

use n to get formula for sequence

u1 u2

written as un =

Generating sequence

Ex un = 4n

First Termsecond term u2 = 4(2) = 8

u3 = 12

Sequence 4 8 12 16 20…..

u1 = 4(1) = 4

Generating sequence

Ex un = n2 + 3

u2 = 22 + 3 = 7

u3 = 32 + 3 = 12

Sequence 4 7 12 19 28….

u1 = 12 + 3 = 4

Finding formulaIf common difference

3 7 11 15 19…..

Term No. Term 1 32 7n

Term No. 1 2 3 4 5

4 4 44 X 4 – 1

4n – 1

Formula Un = 4n – 1

Finding formula

7 12 17 22 27…

Term No. Term 1 72 12n

Term No. 1 2 3 4 5

5 5 55 X 5 + 2

5n + 2

Formula Un = 5n + 2

Sequences

Sequence 1 4 7 10 13 , , , , , ….

1st term 2nd term nth term? u1 u2

written as un =

Generating sequence

Ex un = 3n + 4

First Termsecond term u2 = 3(2) + 4 = 10

u3 = 13

Sequence 7 10 13 16…..

u1 = 3(1) + 4 = 7

Finding formulaIf common difference

2 9 16 23 30…..

Term No. Term n

Term No. 1 2 3 4 5

7 7 7 7X 7 – 5

7n – 5

Formula Un = 7n – 5

Key Questions1.Find values of u1, u2 and u6 for the

sequence un = 4n – 3

u1 = 1, u2 = 5, u6 = 21

2.Find a formula for the nth term of the sequence 9 , 13 , 17 , 21 , 25…un = 4n + 5

What is to be learned?

• What a recurrence relation is• How to find the formula for a sequence as

a recurrence relation• How to generate a sequence, given the

recurrence relation formula

Recurrence Relations

2 8 14 20 26

u6 = u5 + 6

u7 = u6 + 6

un = un-1 + 6

or un+1 = un + 6

u5 …..un

Un = 6n – 4

Generating Sequence using Recurrence Relation

un+1 = un + 3

u2 = 5 + 3 = 8

u3 = 8 + 3 =11

Sequence 5 8 11 14……

u1 = 5

Generating Sequence using Recurrence Relation

un+1 = 3un

u2 = 3(2) = 6

u3 = 3(6) = 18

Sequence 3 6 18 54…..

u1 = 2

Generating Sequence using Recurrence Relation

un+1 = 3un – 2

u2 = 3(2) – 2 = 4

u3 = 3(4) – 2 =10

Sequence 2 4 10 28……

u1 = 2

Finding Recurrence Relation

4 11 18 25 32……

un+1 = un + 7 u1 = 4

Key Questions1.Find the first four terms of recurrence

relation un+1 = un – 4 , u1 = 10

10 , 6 , 2 , -2

2.Find a recurrence relation for this sequence 7 , 11 , 15 , 19 …un+1 = un + 4 , u1 = 7