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
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
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
____
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
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pens you realize quite how important
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