This section is on the basics of sequences. But what is a sequence?
Sequence: function whose domain is an ordered set of natural numbers
There are two ways to define sequences.
Explicit form:
Will tell you any term
The first five terms of the sequence are...
|
n
|
1
|
2
|
3
|
4
|
5
|
|
an
|
1
|
3
|
5
|
7
|
9
|
Recursive form:
All terms are defined using previous terms
a1
= 1
ak+1
= ak + 2
The first five terms of the sequence are...
|
k
|
1
|
2
|
3
|
4
|
5
|
|
ak
|
1
|
3
|
5
|
7
|
9
|
It's the same sequence as before, but it's written differently.
Some common sequences we may see are....
n2:
1, 4, 9, 16, 25…
n3:
1, 8, 27, 64, 125…
2n:
2, 4, 8, 16, 32…
3n:
3, 9, 27, 81…
n!
(factorial): 1, 2, 6, 24, 120…
Fibonacci:
1, 1, 2, 3, 5, 8, 13, 21…
So, it wasn't very long but that's the introduction to sequences!
Carly
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