Slide 2:
Sequence: an ordered set of numbers
Infinite Sequence: a sequence which continues indefinitely
- represented by “…”
Term: each individual number in the sequence
- represented by an
Nth Term/General Term: a rule that describes the sequence
Slide 3:
Explicit Sequences: a sequence in which the general term is based on
the number of the term to be found
To find the value of the terms, simply substitute into the general term.
Find the 1st 3 terms and the 10th term.
An = 2n – 1 2. A1 = 21 – 1 = 1
A2 = 22 – 1 = 3
A3 = 23 – 1 = 7
A10 = 210 - 1
Slide 4:
Find the general term for each sequence.
2, 4, 6, 8, 10, …
Try to identify a “formula” based on the value of the term.
In other words, how do I get a “2” using a “1” since it is the first term?
How do I get a “4” using a “2”, a “6” using a “3”?
You keep multiplying the number of the term by 2 so…
an = 2n
2.
When you have a symbol, use that in your general form. Focus on…
A “3” from a “1”, a “4” from a “2”, a “5” from a “3”
Slide 5:
Recursive Sequence: sequence in which the next term is based on the
previous term
Find the first four terms of each sequence.
a1 = 0 2. a1= 4
an = an-1 + 4 an = 2an-1
a1 = 0 a1 = 4
a2 = 0 + 4 = 4 a2 = 2(4) = 8
a3 = 4 + 4 = 8 a3 = 2(8) = 16
a4 = 8 + 4 = 12 a4 = 2(16) = 32
Slide 6:
Find the recursive formula for the following sequences.
3, 7, 11, …
In this case, you need to determine what you need to do to the first term
to get the second. In other words, what do you do to 3 to get 7?
You add 4 so…
a1 = 3 (you need to state the “starting point”)
an = an-1 + 4 (Think of “an-1” as meaning “previous term”)