This document discusses sequences, which are sets of terms in a definite order obtained by some rule. A sequence can be either finite, ending after a certain number of terms, or infinite, continuing indefinitely. Examples of sequences include the sequence of odd numbers 1, 3, 5, 7, etc. and recurrence relations, which define the first term and the relation between successive terms, such as the sequence 5, 8, 11, 14, etc. The document provides examples and strategies for finding the rule that defines a given sequence, such as looking for a constant difference, signs that alternate, or powers of numbers.

1. 1

3. A sequence is a set of terms, in a
definite order, where the terms are
obtained by some rule.
A finite sequence ends after a
certain number of terms.
An infinite sequence is one that
continues indefinitely.

4. For example: 1, 3, 5, 7, …
(This is a sequence of odd numbers)
1st term = 2 x 1 – 1 = 1
2nd term = 2 x 2 – 1 = 3
3rd term = 2 x 3 – 1 = 5
nth term = 2 x n – 1 = 2n - 1
. .
. .
. .
+ 2
+ 2

5. NOTATION
1st term = u
2nd term = u
3rd term = u
nth term = u
. .
. .
. .
1
2
3
n

6. OR
1st term = u
2nd term = u
3rd term = u
nth term = u
. .
. .
. .
0
1
2
n-1

7. FINDING
THE FORMULA FOR
THE TERMS OF
A SEQUENCE

8. A recurrence relation defines the
first term(s) in the sequence and the
relation between successive terms.

9. u = 5
u = u +3 = 8
u = u +3 = 11
u = u +3 = 3n + 2
.
.
.
1
2
3
n+1
For example: 5, 8, 11, 14, …
1
2
n

10. What to look for
when looking for the rule
defining a sequence

11. Constant difference: coefficient of n is the difference
2nd
level difference: compare with square numbers
(n = 1, 4, 9, 16, …)
3rd
level difference: compare with cube numbers
(n = 1, 8, 27, 64, …)
None of these helpful: look for powers of numbers
(2 = 1, 2, 4, 8, …)
Signs alternate: use (-1) and (-1)
-1 when k is odd +1 when k is even
kk
2
3
n - 1

12. EXAMPLE:
Find the next three terms in the sequence 5, 8, 11, 14, …

13. EXAMPLE:
The nth term of a sequence is given by x =
a) Find the first four terms of the sequence.
b) Which term in the sequence is ?
c) Express the sequence as a recurrence relation.
1__
2
nn
1
1024
____

14. EXAMPLE:
Find the nth term of the sequence +1, -4, +9, -16, +25, …

15. EXAMPLE:
A sequence is defined by a recurrence relation of the form:
M = aM + b.
Given that M = 10, M = 20, M = 24, find the value of a and the
value of b and hence find M .
n + 1
1 32
4

16. This powerpoint was kindly donated to
www.worldofteaching.com
http://www.worldofteaching.com is home to over a
thousand powerpoints submitted by teachers. This is a
completely free site and requires no registration. Please
visit and I hope it will help in your teaching.

17. 17
Do you find this slides were useful?
One second of your life , can bring a smile in a girl life
If Yes ,Join Dreams School “Campaign for Female Education”
Help us in bringing a change in a girl life, because “When someone takes
away your pens you realize quite how important education is”.
Just Click on any advertisement on the page, your one click can make her
smile.
Eliminate Inequality “Not Women”
One second of your life , can bring a smile in her life!!
Do you find these slides were useful?
If Yes ,Join Dreams School “Campaign for
Female Education”
Help us in bringing a change in a girl life,
because “When someone takes away your
pens you realize quite how important
education is”.
Just Click on any advertisement on the page,
your one click can make her smile.
We our doing our part & u ?
Eliminate Inequality “Not Women”