1. Composition of Functions
Skill Check
Composition of Functions
(After HW Check)

2. Go over homework

3. Composition of Functions
Skill Check
Composition of Functions

4. Sequences
A sequence is a function whose domain is a set of consecutive whole numbers. So the domain in any sequence is {1,2,3,4…} The values in the range are called the terms of the sequence. A sequence can be specified by an equation or a rule.

5. Arithmetic Sequence
A sequence of terms that have a common difference between them

6. Determine if the sequence is arithmetic.
Example:
-22, -15, -8, -1, …
Arithmetic
d = 7

7. Determine if the sequence is arithmetic.
Example:
½, ¼, 1/8, 1/16, …
Not Arithmetic

8. Determine if the sequence is arithmetic.
Example:
7, 4, 1, -2, -5
Arithmetic
d = -3

9. Explicit Formula
Formula used to find the nth term of a sequence

10. Explicit Formula for Arithmetic Sequence
Before:
After:

11. Find the common difference, the explicit formula (check your answer), and the tenth term.
3, 9, 15, 21, …
d = 6
an = 6n – 3
a10 = 57

12. Find the common difference, the explicit formula (check your answer), and the twentieth term.
Another way to look at it: What do the pieces mean?
7, 4, 1, -2, …
What would it look like if you drew it?
What would the slope be?
How would you get the y-intercept?
So:
The difference between the numbers. In this case, -3.
Look at the number that would be BEFORE the first. In this case, 10 would come BEFORE 7.

13. Find the common difference, the explicit formula (check your answer), and the sixteenth term.
17, 21, 25, …

14. Applications
The marching band has 14 marchers in the front row, 16 in the second row, 20 in the fourth row, and so on. How many marchers are in the 15th row?

15. Applications
Several friends want to go on a rafting trip. The cost of the trip per person is in the chart.
How much would it cost for 9 people to go?
Passengers 1 2 3 4
Cost
$75
$100
$125
$150

16. Explicit vs. Recursive Notation

17. Explicit vs. Recursive Notation
Explicit Notation – Lets you find any term immediately without using any others
Recursive Notation – Defines a given term based on the previous term

18. (This one doesn’t simplify)
Arithmetic Sequences
Explicit Notation:
Recursive Notation:
(This one doesn’t simplify)

19. Convert from explicit to recursive:
Write out the first 3 terms
Find the difference and the first term
Plug them into the formula
11, 14, 17,…
d = 3; a1 = 11

20. Convert from recursive to explicit:
Write out the first 3 terms
Find the slope and y-intercept (go back one for a0)
Plug them into the slope-intercept formula
5, 2, -1,…
m = -3; b = 8 (which would be before the 5)

21. Classwork & Homework Worksheets