1. Sequences

2. What is to be learned How to find the formula for a sequence
How to generate a sequence, given the formula
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

3. Sequence n any term? nth term 3 5 7 9 11 Term Number 1 2 3 4 5
Term Number n
, , , , , ….
2nd term
1st term
u u2
use n to get formula for sequence
written as un =

4. Generating sequence Ex un = 4n First Term second term u2 = 4(2) = 8 u1
= 4(1) = 4

5. Generating sequence Ex un = n2 + 3 u2 = 22 + 3 = 7 u1 = 12 + 3 = 4

6. Finding formula If common difference 3 7 11 15 19….. Term No. Term 1 3
…..
Term No. Term n
Term No.
X 4
– 1
4n - 1
Formula Un = 4n - 1

7. Finding formula 7 12 17 22 27… Term No. Term 1 7 2 12 n Term No.…
Term No. Term n
Term No.
X 5
+ 2
5n + 2
Formula Un = 5n + 2

8. Sequences Sequence 1 4 7 10 13 , , , , , …. 2nd term nth term?
, , , , , ….
2nd term
nth term?
1st term
u u2
written as un =

9. Generating sequence Ex un = 3n + 4 First Term
second term u2 = 3(2) + 4 = 10
u3 = 13
Sequence ….. u1
= 3(1) + 4 = 7

10. Finding formula If common difference 2 9 16 23 30….. Term No. Term n
…..
Term No. Term n
Term No.
X 7
– 5
7n - 5
Formula Un = 7n - 5

11. Recurrence Relations 2 8 14 20 26 u5 …..un u6 = u5 + 6 u7 = u6 +6
u6 = u5 + 6
u7 = u6 +6
un = un-1 + 6
or un+1 = un + 6 u5
…..un

12. Generating Sequence using Recurrence Relation
un+1 = un + 3
u2 = = 8
u3 = =11
Sequence ……
u1 = 5

13. Generating Sequence using Recurrence Relation
un+1 = 3un - 2
u2 = 3(2) – 2 = 4
u3 = 3(4) – 2 =10
Sequence ……
u1 = 2

14. Finding Recurrence Relation……
un+1 = un + 7
u1 = 4