1. Recognizing Patterns and Sequences
Lesson 1

2. Sequence
A sequence is a pattern of an ordered list of elements (numbers, figures in a picture, letters etc.)
A term in the sequence is an individual item / element of the list.
Examples:
3, 5, 7, 9… J, F, M, A, M, J, J,
The “…” indicates that the pattern continues.
Infinite sequences continue on forever (…)
Finite sequences terminate (stop)

3. A sequence is a function whose:3 5 7 9 3 5 7 9
A sequence is a function whose:
-domain is a subset of integers (the natural #s)
-range are the terms themselves (the actual number or item in the list)
Think: the input/x-value/domain is 1, 2, 3, 4, etc for how far in the list it is
the output/y-value/range are the actual numbers in the pattern

4. Term Notation
We use subscript to identify each term of the sequence starting at 1:
a1 is used to identify the 1st term in the sequence.
a12 is used to identify the 12th term in the sequence.
an is used to identify the nth term in the sequence.
Example sequence
1, 2, 4, 8, 16, 32
So a1 = 1, a2 = 2, a3 = 4, a4 = 8 etc.
Mean Same Thing

5. Describe the pattern in the sequence
Example 1:
2, 8, 32, 128, …
Multiply by 4 each time
first term a1=2
Example 2:
555, 55.5, 5.55, .555, …
Divide by 10 each time
first term a1=555
List the next 3 terms in the sequence
Example 3:
5, 2.5, 0, …
Add -2.5 (like subtract 2.5)
5, 2.5, 0, -2.5, -5, -7.5
Example 4:
32, 16, 8, 4,…
Multiply by ½ (like divide by 2)
32, 16, 8, 4, 2, 1, ½